Question

If 2x cube + ax squared + bx - 2 leaves the remainder 7 and - 20 when divided by 2x - 3 and x + 3 respectively. Find the value of a and b

Answer 1

2x³ + ax ² + bx - 2

If P(x) is polynomial and D(x) is divisor and q(x) is quotient and R is remainder than

P(x) = D(x)*q(x) + R

If at x = a D(x) = 0 than P(a) = 0+R = R

We have P(x) = 2x³ + ax ² + bx - 2

D(x) = 2x-3 and R = 7

At x = 3/2 D(x) = 0 It means P(3/2) = R = 7

2*(3/2)³+a*(3/2)² +b*3/2 -2 = 7

27/4 + 9a/4 +3b/2 = 9

27+9a+6b = 9*4 = 36

9a+6b = 9 .....................1


Similarly when D(x) = x+3 and R = -20

At x = -3, P(-3) = R = -20

2*(-3)³+a*(-3)² +b*(-3) -2 = -20

-54+9a-3b-2 = -20

9a-3b = 36 ......................................2


Solve quation 1 and 2

9a+6b = 9

9a-3b = 36

Subtract equation 1 from 2 we will get

9b = -27

b = -3

put value of b in equation 1 we will get

9a-6*3 = 9

9a = 27

a =3

Answer : a=3 and b= -3