Question

If 1/2 is a root of the quadratic equation x²-mx-5/4=0 , then the value of m is? ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

$\displaystyle \sf{ \frac{1}{2} \: \: is \: a \: root \: of \: the \: quadratic \: equation }$

$\displaystyle \sf{ {x}^{2} - mx - \frac{5}{4} = 0\: }$

TO DETERMINE

The value of m

CALCULATION

$\because \: \displaystyle \sf{ \frac{1}{2} \: \: is \: a \: root \: of \: the \: quadratic \: equation }$

$\displaystyle \sf{ {x}^{2} - mx - \frac{5}{4} = 0\: }$

So

$\displaystyle \sf{ { \bigg( \frac{1}{2} \bigg)}^{2} - m \times \frac{1}{2} - \frac{5}{4} } = 0$

$\implies \: \displaystyle \sf{ \frac{1}{4} - \frac{m}{2} - \frac{5}{4} } = 0 \:$

$\implies \: \displaystyle \sf{ - \frac{m}{2} - 1 } = 0 \:$

$\implies \: \displaystyle \sf{ - \frac{m}{2} = 1 } \:$

$\implies \: \displaystyle \sf{ m = - 2 }$

RESULT

Hence the value of m is - 2

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