Question

If both (x-2) & (x-1/2) are factors of px2+5x+r, show that p = r​

Answer 1

Step-by-step explanation:

x-2=0

x=2

substituting in equation

px2+5x+r=0

4p+10+r=0(1)

x-1/2=0

x=1/2

substituting in equation

p+4r+10=0(2)

by solving equations 1 and 2

p=q= -2

therefore,p=q

hope it helps you.

Answer 2

As both are the factors of the given polynomials, both must be zero for x = 2 and 1/2.   Using factor theorem:

 If x - 2 is factor: f(2) = 0

⇒ p(2)² + 5(2) + r = 0

⇒ 4p + 10 + r = 0          ...(1)

 If x - 1/2 is factor: f(1/2) = 0

⇒ p(1/2)² + 5(1/2) + r = 0

⇒ p/4 + 5/2 + r = 0

⇒ p + 10 + 4r = 0         ...(2)

   Subtract (1) from (2), we get:

⇒ 3p - 3r = 0

⇒ 3p = 3r

⇒ p = r      proved