If 2x^2 + 5x - 3 = 0 and x > 0, what is the value of x? — GMAT

If $2x^2 + 5x - 3 = 0$ and $x > 0$ , what is the value of $x$ ?

Answer: 0.5

The value of

x

is 0.5.

Factoring the quadratic equation

2x^2 + 5x - 3 = 0

yields

(2x - 1)(x + 3) = 0

. Setting each linear factor equal to zero gives two possible solutions for

x

x = 0.5

and

x = -3

. Because the problem stipulates that

x > 0

, the negative solution is discarded, leaving

x = 0.5

Factor the quadratic expression

(2x - 1)(x + 3) = 0

Splitting the middle term

5x

into

6x - x

allows grouping to factor by grouping.

Find the roots of the equation

x = 0.5

x = -3

By the zero-product property, if the product of two factors is zero, at least one factor must be zero.

Apply the positivity constraint

x > 0

x = 0.5

The root

x = -3

violates the given condition that

x

must be strictly greater than zero.

Solving quadratic equations by factoring and applying domain constraints

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