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Solve the given quadratic equation $2 x^{2} + 5 x + 2 = 0$

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- \frac{2}{3}

and −6

- \frac{1}{2}

and −2

- \frac{1}{4}

and −3

\frac{1}{2}

and 2

answer is B.

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Detailed Solution

Given quadratic equation,

2 x^{2} + 5 x + 2 = 0

On comparing this equation with

a x^{2} + bx + c = 0

we get,

a = 2, b = 5, c = 2

Here, the value of discriminant,

D = b^{2} - 4 ac

= (5)^{2} - 4 \times 2 \times 2

= 25 - 16

= 9

x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a}

x = \frac{- 5 \pm \sqrt{9}}{2 \times 2}

x = \frac{- 5 \pm 3}{4}

Taking positive sign,

x = \frac{- 5 + 3}{4}

x = - \frac{1}{2}

Tanking negative sign,

x = \frac{- 5 - 3}{4}

x = - 2

So, the roots of the given equation are

- \frac{1}{2}

and −2.
Option 2 is correct.

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