Quadratic Inequality

Algebra Level 1

The graph above is a quadratic function, y = x 2 + k x − 2 y =x^2+kx-2 for some constant k k . What is the solution to the quadratic inequality x 2 + k x − 2 < 0 x^2 + kx-2 < 0 ?

Clarification: The graph intersects the x x -axis at x = 1 x=1 .

− 1 < x < 2 -1<x<2 − 2 < x < 1 -2<x<1 − 1 < x < 1 -1<x<1 − 2 < x < 2 -2<x<2

Kumar Gupta by Kumar Gupta , 23, India

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3 solutions

As x = 1 x=1 is solution to the ecuation we can replace the point ( 1 , 0 ) (1,0) in the parabole, where we get k = 1 k=1 , so the parabola gets y = ( x − 1 ) ( x + 2 ) y=(x-1)(x+2) and the interval where the parabola gets negative is ( − 2 , 1 ) (-2,1)

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Yeah I used synthetic division to find k

Jerry McKenzie - 4 years, 2 months ago
John Taylor
Nov 28, 2015

From Vieta's formula we know that the product of the roots of the equation is c / a = − 2 c/a = -2 . Therefore the other root must be − 2 -2 . Since the graph shown has y values of less than 0 0 from − 2 < x < 1 -2<x<1 answer choice 2 is correct.

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Surina M
Dec 22, 2015

x^2 + kx - 2 < 0 if we are given that the line cuts the x axis at 1, then one of the factorised brackets must be: (x-1) The only other bracket that would satisfy this equation would be: (x+2) Therefore: (x-1)(x+2) < 0 And so the line also crosses the x axis at -2 which means whenever x is bigger than -2 and smaller than 1, y will be less than 0.

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