Question

For what real values of x is the expression 2x^2+5x-3 negative?

Quadratic Equations
${2x}^{2} + 5x - 3$

Answer 1

Please see the attachment

Answer 2

Concept introduction:

In the case of quadratic equation, the real value of x and the determining number or expression depends on the nature of the equation. For example, in case of an expression like 2x^2+5x-3, the value of x cannot be negative.

Given:

We have been given a quadratic equation and expression 2x^2+5x-3

To find:

We have to find the real value of x and for what real values of x this this expression negative.

Solution:

According to the question,

2x^2+5x-3 < 0

or, 2x^2+6x-x-3<0

or, 2x(x+3)-1(x+3)<0

or, (x+3)(2x-1)<0

Therefore, -3<x<1/2

Final answer:

For the values of -3 and 1/2 the expression cannot be negative.

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