Question

If both x - 2 and 2x – 1 are the factors of px2 + 5x +r, show that p = r​

Answer 1

QUESTION:-

If both x - 2 and 2x – 1 are the factors of px ²+ 5x +r, show that p = r​

TO PROVE:-

p=r

EXPLANATION:-

LET P(x)= px ²+ 5x +r

and g(x)= px ²+ 5x +r

no x-2=0

x=2

putting x=2 in P(x):-

P(x)=p(2)² +5(2)+r

P(x)=4p+10+r

P(x)=0  since x-2 is factor of it so remainder is zero,

4p+10+r=0

4p+r=-10_______________eq-1

now

g(x)=px ²+ 5x +r

2x-1=0

x=1/2

putting x=1/2 in g(x)

$g(1/2)=p(\frac{1}{2} ^2)+\frac{5}{2} +r$

g(1/2)=p+10+4r

g(1/2)=0

4r+p=-10________________eq-2

subtracting eq-1 from eq-2

(4p−p)+(r−4r)=−10−(−10)

⇒3p−3r=−10+10

⇒3p−3r=0

⇒3p=3r

⇒p=r

Hence, p=r is proved.