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If the roots of the given equation $2 x^{2} + 3 (γ - 2) x + γ + 4 = 0$ be equal in magnitude but opposite in sign, then value of $γ$ is

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4

3

answer is B.

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Detailed Solution

Given, the equation is

2 x^{2} + 3 (γ - 2) x + γ + 4 = 0 .

We need to find the value of

γ

.
We know that equation

Then sum of roots

= - \frac{b}{a} .

Let us assume that

α, β

are the roots of the given equation.

∴ α + β = - \frac{3 (γ - 2)}{2}

But from the given data,

α = - β

∴ - β + β = - \frac{3 (γ - 2)}{2}

\Rightarrow 0 = - \frac{3 (γ - 2)}{2}

\Rightarrow 0 \times \frac{2}{- 3} = (γ - 2)

\Rightarrow 0 = γ - 2

\Rightarrow γ = 2

Hence, the correct option is 2.

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