Question

If (x-2) and (x-1/2) are factor of Px2+5x+r then show that P=r

Answer 1

Given equation :- Px² + 5x + r

given roots :- ( x - 2 ) = 0
x = 2

( x - 1/2 ) = 0
x = 1/2


As we know that


product of zeros =

$\frac{constant \: term}{coefficient \: of \: {x}^{2} }$

2 × 1/2 = r / P

1 = r/P

P = r



Hence proved !!