Question

if (x-2) and (x-1/2) are factors of px x ka square +5x+r then show that p=r

Answer 1

$\mathfrak{\huge{Hi !}}$

$\sf{\underline{Zeroes}}\tt{ = 2, \frac{1}{2}}$

$\sf{\underline{Polynomial}}\tt{= px^{2} + 5x + r}$

Equation with zero = 2

=》 $\tt{(2)^{2}p + 5(2) + r = 0}$

=》 $\tt{r = -4p - 10}$

Equation with zero = 1/2

=》 $\tt{\frac{1}{2}^{2} + 5 \frac{1}{2} + r = 0}$

=》 $\tt{r = -\frac{p}{4} - \frac{5}{2}}$

r = r

=》 $\tt{-4p + \frac{p}{4} = 10 - \frac{5}{2}}$

=》 $\tt{\frac{-16p+p}{4} = \frac{20-5}{2}}$

=》 $\tt{-15p = 30}$

=》 $\tt{p = (-2)}$ ...(1)

$\tt{r = \frac{2}{4} - \frac{5}{2}}$

=》 $\tt{r = (-2)}$ ...(2)

$\underline{\sf{By\:(1)\:and\:(2),\:we\:can\:say:}}$

$\bf{p = r}$

Hence Proved !!