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What are the roots of the given quadratic equation $2 x ² + x – 4 = 0$ ?

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x = 33 − 1 4

and

x = − 1 − 33 4

x = 33 + 1 4

and

x = − 1 − 33 4

x = − 33 − 1 4

and

x = 1 − 33 4

x = 33 − 1 2

and

x = − 1 − 33 2

answer is A.

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Detailed Solution

Given equation is

2 x 2 + x − 4 = 0.

Let us solve the given equation using completing the square method.
Adding 4 on both the sides, we get

2 x 2 + x − 4 + 4 = 0 + 4 ⇒ 2 x 2 + x = 4

On dividing the whole equation by the coefficient of

x 2

i.e., 2, we get

⇒ 2 x 2 2 + x 2 = 42

⇒ x 2 + x 2 = 2

Coefficient of term

x = 12

.
Half of the coefficient of x is,

⇒ 12 × 12 ⇒ 14

Add the square of half of the coefficient of term ‘x’, on both sides of the equation.

x 2 + x 2 + 142 = 2 + 142

Since,

a 2 + 2 a b + b 2 = (a + b) 2

We get,

x + 14 2 = 2 + 116 ⇒ x + 14 2 = 32 + 1 16 ⇒ x + 14 2 = 3316

Take the square root,

⇒ x + 14 = ± 334 ⇒ x = ± 334 − 14 ⇒ x = 334 − 14 ⇒ x = 33 − 1 4 o r ⇒ x = − 33 4 − 14 ⇒ x = − 1 − 33 4

The roots or solution for the quadratic equation

2 x 2 + x − 4 = 0

are

x = 33 − 1 4

and

x = − 1 − 33 4

.
Therefore, the correct option is 1.

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