Advertisements
Advertisements
Question
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Solution
f(x) = 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8
x – 2 = 0 `\implies` x = 2
Since, x – 2 is a factor of f(x), remainder = 0.
2(2)5 – 6(2)4 – 2a(2)3 + 6a(2)2 + 4a(2) + 8 = 0
64 – 96 – 16a + 24a + 8a + 8 = 0
–24 + 16a = 0
16a = 24
a = 1.5
APPEARS IN
RELATED 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.
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x2 – Kx + 6 = 0. Also, find the other root of the equation.
If x – 3 is a factor of p(x), then the remainder is
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
If mx2 – nx + 8 has x – 2 as a factor, then ______.
