Advertisements
Advertisements
Questions
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
If (x – 2) is a factor of 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Advertisements
Solution
Since (x – 2) is a factor of polynomial 2x3 + ax2 + bx – 14, we have
2(2)3 + a(2)2 + b(2) – 14 = 0
⇒ 16 + 4a + 2b – 14 = 0
⇒ 4a + 2b + 2 = 0
Dividing the entire equation by 2,
⇒ 2a + b = –1 ...(1)
On dividing by (x – 3), the polynomial 2x3 + ax2 + bx – 14 leaves remainder 52,
2(3)3 + a(3)2 + b(3) – 14 = 52
⇒ 54 + 9a + 3b – 14 = 52
⇒ 9a + 3b = 52 – 40
⇒ 9a + 3b = 12
Dividing the entire equation by 3,
⇒ 3a + b = 4 ...(2)
Subtracting (1) and (2), we get
2a + b = –1
3a + b = 4
– – –
–a = –5
Substituting a = 5 in (1), we get
2 × 5 + b = –1
⇒ 10 + b = –1
⇒ b = –11
Hence, a = 5 and b = –11.
APPEARS IN
RELATED QUESTIONS
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.
