The expression 2x^3 + ax^2 + bx-2 leaves remainder 7 and 0 when divided by 2x-3 and x+2 respectively.Calculate the values of a and b.
Answers
Answer:
a = -3/5 and b = -39/5
Step-by-step explanation:
(i) 2x-3 = 0
x = 3/2
by using remainder thearom
put the value of x in f(x) 2x^3 + ax^2 + bx-2
f(3/2) = 2 ×( 3/2)^3 + a × (3/2)^2 + b × 3/2 -2 = 7
= 2 × 27/8 + a × 9/4 + 3b/2 - 2 = 7
= 27/4 + 9a/4 + 3b/2 = 7 -2
= (9a + 6b)/4 = 5 - 27/4 = 9a + 6b = -7
= 3a + 2b = -21 ---(1)
(ii) x + 2 = 0
x = -2
by using remainder thearom
put the value of x in f(x) 2x^3 + ax^2 + bx-2
f(-2) = 2(-2)^3 + a(-2)^2 + (-2b) -2 = 0
= -16 + 4a - 2b - 2 = 0
= 4a - 2b = 18
= 2a - b = 9 -----(2)
solving eq. 1 and 2 we get the value of
a = -3/5 and b = -39/5