Question

Solve the following
If $\frac{1}{2}$ is a root of equation $x^2+px-\frac{5}{4}=0$ then find the other root of Quadratic equation

Answer 1

given quadratic equation is $x^2+px-5/4$

therefore the sum of roots of this equation is $\frac{-p}{1}=-p$

given $1$ root is $\frac{1}{2}$ let the other root be $x$

as $\frac{1}{2}$ is a root

$\Rightarrow {\left(\frac{1}{2}\right)}^2+p\left(\frac{1}{2}\right)-\frac{5}{4}=0\Rightarrow p=2$

sum of roots $=x+\frac{1}{2}=-p=-2$

therefore the other root is $-2-\frac{1}{2}=-2.5$