How do I solve this quadratic-intersection question?
My question: Find the values of $k$ for which the parabola $y=2x^2+kx+9$ does not intersect the line $y=2x+2$.
My workings: I am thinking of using the discriminant rule to this where Δ < 0, however, I am unsure if it is applicable. As far as i know, the Δ shows the number of solutions and does the graph touches x-axis or not.
Can someone show some working outs or at least give me some hints where and how i should approach this question?
Thank you very much!
algebra-precalculus inequality quadratics
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
asked Nov 21 '18 at 6:51
Tfue
1309
add a comment |
My question: Find the values of $k$ for which the parabola $y=2x^2+kx+9$ does not intersect the line $y=2x+2$.
My workings: I am thinking of using the discriminant rule to this where Δ < 0, however, I am unsure if it is applicable. As far as i know, the Δ shows the number of solutions and does the graph touches x-axis or not.
Can someone show some working outs or at least give me some hints where and how i should approach this question?
Thank you very much!
algebra-precalculus inequality quadratics
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
asked Nov 21 '18 at 6:51
Tfue
1309
add a comment |
My question: Find the values of $k$ for which the parabola $y=2x^2+kx+9$ does not intersect the line $y=2x+2$.
My workings: I am thinking of using the discriminant rule to this where Δ < 0, however, I am unsure if it is applicable. As far as i know, the Δ shows the number of solutions and does the graph touches x-axis or not.
Can someone show some working outs or at least give me some hints where and how i should approach this question?
Thank you very much!
algebra-precalculus inequality quadratics
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
asked Nov 21 '18 at 6:51
Tfue
1309
My question: Find the values of $k$ for which the parabola $y=2x^2+kx+9$ does not intersect the line $y=2x+2$.
My workings: I am thinking of using the discriminant rule to this where Δ < 0, however, I am unsure if it is applicable. As far as i know, the Δ shows the number of solutions and does the graph touches x-axis or not.
Can someone show some working outs or at least give me some hints where and how i should approach this question?
Thank you very much!
algebra-precalculus inequality quadratics
algebra-precalculus inequality quadratics
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
asked Nov 21 '18 at 6:51
Tfue
1309
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
asked Nov 21 '18 at 6:51
Tfue
1309
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
edited Nov 21 '18 at 12:53
Martin Sleziak
44.7k7115270
44.7k7115270
asked Nov 21 '18 at 6:51
Tfue
1309
asked Nov 21 '18 at 6:51
Tfue
1309
asked Nov 21 '18 at 6:51
Tfue
1309
1309
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Hint: Your idea of discriminant is good. Substitute for $y$ in the quadratic using the equation of the line. Now if there are solution(s) for $x$, there is intersection, so set the discriminant to negative.
--
Details: We need to ensure there are no solutions for $2x+2 = 2x^2+kx+9$. $iff 2x^2+(k-2)x+7 neq 0 iff (k-2)^2<4cdot2cdot7$ $iff |k-2|<2sqrt{14} iff k in (2-2sqrt{14}, 2+2sqrt{14})$.
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
Macavity do mean 'discriminant' because i don't know what determinant is and also basically you want me to equate both of them?
– Tfue
Nov 21 '18 at 8:16
Sorry sir can you please help? I still do not understand what you meant in second line 'setting determinant to negative'
– Tfue
Nov 21 '18 at 10:39
@Tfue: You are right, it I the discriminant... Have added to the answer I gave.
– Macavity
Nov 21 '18 at 11:45
Cheers mate !!!!
– Tfue
Nov 21 '18 at 11:52
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
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oldest
votes
active
oldest
votes
Hint: Your idea of discriminant is good. Substitute for $y$ in the quadratic using the equation of the line. Now if there are solution(s) for $x$, there is intersection, so set the discriminant to negative.
--
Details: We need to ensure there are no solutions for $2x+2 = 2x^2+kx+9$. $iff 2x^2+(k-2)x+7 neq 0 iff (k-2)^2<4cdot2cdot7$ $iff |k-2|<2sqrt{14} iff k in (2-2sqrt{14}, 2+2sqrt{14})$.
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
Macavity do mean 'discriminant' because i don't know what determinant is and also basically you want me to equate both of them?
– Tfue
Nov 21 '18 at 8:16
Sorry sir can you please help? I still do not understand what you meant in second line 'setting determinant to negative'
– Tfue
Nov 21 '18 at 10:39
@Tfue: You are right, it I the discriminant... Have added to the answer I gave.
– Macavity
Nov 21 '18 at 11:45
Cheers mate !!!!
– Tfue
Nov 21 '18 at 11:52
add a comment |
Hint: Your idea of discriminant is good. Substitute for $y$ in the quadratic using the equation of the line. Now if there are solution(s) for $x$, there is intersection, so set the discriminant to negative.
--
Details: We need to ensure there are no solutions for $2x+2 = 2x^2+kx+9$. $iff 2x^2+(k-2)x+7 neq 0 iff (k-2)^2<4cdot2cdot7$ $iff |k-2|<2sqrt{14} iff k in (2-2sqrt{14}, 2+2sqrt{14})$.
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
Macavity do mean 'discriminant' because i don't know what determinant is and also basically you want me to equate both of them?
– Tfue
Nov 21 '18 at 8:16
Sorry sir can you please help? I still do not understand what you meant in second line 'setting determinant to negative'
– Tfue
Nov 21 '18 at 10:39
@Tfue: You are right, it I the discriminant... Have added to the answer I gave.
– Macavity
Nov 21 '18 at 11:45
Cheers mate !!!!
– Tfue
Nov 21 '18 at 11:52
add a comment |
Hint: Your idea of discriminant is good. Substitute for $y$ in the quadratic using the equation of the line. Now if there are solution(s) for $x$, there is intersection, so set the discriminant to negative.
--
Details: We need to ensure there are no solutions for $2x+2 = 2x^2+kx+9$. $iff 2x^2+(k-2)x+7 neq 0 iff (k-2)^2<4cdot2cdot7$ $iff |k-2|<2sqrt{14} iff k in (2-2sqrt{14}, 2+2sqrt{14})$.
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
Hint: Your idea of discriminant is good. Substitute for $y$ in the quadratic using the equation of the line. Now if there are solution(s) for $x$, there is intersection, so set the discriminant to negative.
--
Details: We need to ensure there are no solutions for $2x+2 = 2x^2+kx+9$. $iff 2x^2+(k-2)x+7 neq 0 iff (k-2)^2<4cdot2cdot7$ $iff |k-2|<2sqrt{14} iff k in (2-2sqrt{14}, 2+2sqrt{14})$.
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
edited Nov 21 '18 at 12:52
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
answered Nov 21 '18 at 7:05
Macavity
35.1k52453
35.1k52453
Macavity do mean 'discriminant' because i don't know what determinant is and also basically you want me to equate both of them?
– Tfue
Nov 21 '18 at 8:16
Sorry sir can you please help? I still do not understand what you meant in second line 'setting determinant to negative'
– Tfue
Nov 21 '18 at 10:39
@Tfue: You are right, it I the discriminant... Have added to the answer I gave.
– Macavity
Nov 21 '18 at 11:45
Cheers mate !!!!
– Tfue
Nov 21 '18 at 11:52
add a comment |
Macavity do mean 'discriminant' because i don't know what determinant is and also basically you want me to equate both of them?
– Tfue
Nov 21 '18 at 8:16
Sorry sir can you please help? I still do not understand what you meant in second line 'setting determinant to negative'
– Tfue
Nov 21 '18 at 10:39
@Tfue: You are right, it I the discriminant... Have added to the answer I gave.
– Macavity
Nov 21 '18 at 11:45
Cheers mate !!!!
– Tfue
Nov 21 '18 at 11:52
Macavity do mean 'discriminant' because i don't know what determinant is and also basically you want me to equate both of them?
– Tfue
Nov 21 '18 at 8:16
Macavity do mean 'discriminant' because i don't know what determinant is and also basically you want me to equate both of them?
– Tfue
Nov 21 '18 at 8:16
Sorry sir can you please help? I still do not understand what you meant in second line 'setting determinant to negative'
– Tfue
Nov 21 '18 at 10:39
Sorry sir can you please help? I still do not understand what you meant in second line 'setting determinant to negative'
– Tfue
Nov 21 '18 at 10:39
@Tfue: You are right, it I the discriminant... Have added to the answer I gave.
– Macavity
Nov 21 '18 at 11:45
@Tfue: You are right, it I the discriminant... Have added to the answer I gave.
– Macavity
Nov 21 '18 at 11:45
Cheers mate !!!!
– Tfue
Nov 21 '18 at 11:52
Cheers mate !!!!
– Tfue
Nov 21 '18 at 11:52
add a comment |
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