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If one root of equation $2 x^{2} + ax + 6 = 0$ is 2 then a=?

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7

- 7

\frac{7}{2}

- \frac{7}{2}

answer is B.

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Detailed Solution

Given quadratic equation is,

2 x^{2} + ax + 6 = 0

.
And one root of the given equation is 2.
We know that, if

x = m

is a solution of the equation

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

then

a m^{2} + bm + c = 0

.
Then at

x = 3

2 x^{2} + ax + 6 = 0

⟹ 2 {(2)}^{2} + 2 a + 6 = 0

⟹ 8 + 2 a + 6 = 0

⟹ 2 a + 14 = 0

⟹ 2 a = - 14

⟹ a = - \frac{14}{2}

∴ a = - 7

∴

If one root of the equation

2 x^{2} + ax + 6 = 0

is 2 then

a = - 7

Hence, the correct option is 2.

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