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The equation of a curve is $y=ax^2+5x+a-5$, where $a$ is a constant. In the case where $a=2$, find the set of values of $x$ for which the curve lies completely above the line $y=9$.

I sub $a=2$ and solve using simultaneous equation and get $x=1.5$ and $x=-4$ but I got confused as there is no intersection.

Juan Castaño
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Jayle
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    Hint: you need to solve the inequality $a^2 + 5x + a - 5 > 9$ But then the question is a bit weird, maybe you are asked to find such $a$ for which the curve lies completely above $y = 9$? – junumboxo Jan 19 '21 at 10:24
  • I thought it’s weird too, but it’s given a=2 , ask to find x when curve above line y=9 , does it means that x<-4,x>1.5? – Jayle Jan 19 '21 at 10:35
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    Why don't you just ask the solution of $2x^2+5x-3>9$ ?? –  Jan 19 '21 at 10:35
  • And what do you call "no intersection" ? –  Jan 19 '21 at 10:38
  • The solution will show x>1.5, x>-4 which if I draw the curve out it’s not true as x should be < -4 for y to be above 9. Thus i don’t know how to express the solution correctly – Jayle Jan 19 '21 at 10:41
  • You are not reading the intersections correctly. $x \geq \frac{3}{2}$ and $x \leq -4$ are your solutions. – Math Lover Jan 19 '21 at 10:54

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