# If Both X − 2 and X − 1 2 Are Factors of Px2 + 5x + R, Then - Mathematics

MCQ

If both x − 2 and $x - \frac{1}{2}$ are factors of px2 + 5x + r, then

•  p = r

• p + r = 0

• 2p + r = 0

• p + 2r = 0

#### Solution

As (x - 2)and  (x - 1/2)are the factors of the polynomial px^2 + 5x  + r

i.e.,  f(2) = 0and  f(1/2) = 0

Now,

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

4p + r = -10    ..... (1)

And

f(1/2) = p(1/2)^2 + 5(1/2) + r = 0

p/4 + 5/2 + r = 0

p + 10 + 4x = 0

p+ 4x = -10         ........(2)

From equation (1) and (2), we get

4p + r = p + 4r

3p = 3x

 p = r

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Q 19 | Page 35