Question

If ( x - 2 ) and ( x - 1/2 ) are the factors of the polynomial qx² + 5x + r proce that q = r

Answer 1

x - 2 = 0

x = 2

putting x = 2 in equation

q(4) + 5(2) + r = 0

4q + 10 + r = 0

r = - 10 - 4q                       (1)

x - 1/2 = 0

x = 1/2

putting x = 1/2 in equation

q(1/4) + 5(1/2) + r = 0

q/4 + 5/2 + r = 0

q/4 + 5/2 = - r

q/4 + 5/2 = - ( - 10 - 4q)

q/4 + 5/2 = 10 + 4q

q/4 - 4q = 10 - 5/2

-15q/4 = 15/2

-q/4 = 1/2

q = -2

putting the value of q in (1) -

r = - 10 - 4(-2)

r = - 10 + 8

r = - 2

Hence q = r