Question

pls help maths question class 10 quadratic equation​

Answer 1

$\huge{\underline{\sf{\red{AnsWer\leadsto k=-2}}}}$

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Given:

Quadratic Equation:

$x^2+kx-\dfrac{5}{4}$

Root of the Equation $\dfrac{1}{2}$

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To find k

SoluTion:

We know that

ax²+bx+c

In the Given Quadratic Equation

$a=1 \\ b=k \\ c =\dfrac{-5}{4}$

Sum of Root of a quadratic Equation = $\dfrac{-b}{a}$

Product of Roots of a Quadratic Equation =$\dfrac{c}{a}$

Here Let one root be $\beta$

$\dfrac{1}{2} + \beta = \dfrac{k}{1}\huge{\star}1$

$\dfrac{1}{2} \times \beta = \dfrac{-5}{4} \\ \implies \dfrac{\beta}{2}=\dfrac{-5}{4} \\ \implies \beta = \dfrac{\cancel{-10}}{\cancel{4}} \\ \beta=\dfrac{-5}{2}$

Now,

By putting the Value of $\beta$in the $\star 1$

$\implies \dfrac{1}{2} + \bigg(\dfrac{-5}{2}\bigg) = k \\ \\ \implies \dfrac{1-5}{2} =k \\ \\ \huge{\leadsto{\boxed{k=-2}}}$