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Q.

If $x = \frac{- 1}{2}$ is the root of the equation $x^{2} - mx - \frac{5}{4} = 0$ then value of m is?

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a

-2

b

2

c

-3

d

3

answer is A.

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Detailed Solution

detailed_solution_thumbnail

Given quadratic equation is,

x^{2} - mx - \frac{5}{4} = 0

.

x = \frac{- 1}{2}

is the root of given equation then,

x^{2} - mx - \frac{5}{4} = 0

\Rightarrow {(\frac{- 1}{2})}^{2} - m (\frac{- 1}{2}) - \frac{5}{4} = 0

\Rightarrow \frac{1}{4} + \frac{m}{2} - \frac{5}{4} = 0

\Rightarrow \frac{1 + 2 m - 5}{4} = 0

\Rightarrow \frac{2 m - 4}{4} = 0

\Rightarrow 2 m - 4 = 0

\Rightarrow m = \frac{4}{2}

∴

m = 2

Thus, the value of m is 2.
Hence, option (1) is correct.

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