Question

if both x-2 and x-1/2 are factor of px^2+5x+r show that p=r​

Answer 1

Step-by-step explanation:

Hello Mate!

As given, factors are : ( x - 2 ) and ( x - 1 / 2 ). So value of x = 2 and 1 / 2

p(x) = p{x}^{2} + 5x + rpx

2

+5x+r

0 = p(2)^2 + 5(2) + r

0 = 4p + 10 + r ______(1)

p(x) = p(1/2)^2 + 5(1/2) + r

0 = p / 4 + 5 / 2 + r

0 = ( p + 10 + 4r ) / 4

0 = p + 10 + 4r _____(2)

4p + 10 + r = p + 10 + 4r

4p + r = p + 4r

4p - p = 4r - r

3p = 3r

p = r

\boxed{ Hence\:Proved }

HenceProved

Answer 2

Answer:

yes both p and r will be equal

Step-by-step explanation:

Refer attachment:

putting x=2 and x=1/2

in above equation new equation will be

4p+10+r=0 --------->i

p+10+4r =0------------->ii

after solving both equation 3p=3r

therefore p=r proved.