Advertisements
Advertisements
Question
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
Advertisements
Solution
Let f(x) = (3k + 2)x3 + (k − 1)
2x + 1 = 0
`\implies x = (−1)/2`
Since, 2x + 1 is a factor of f(x), remainder is 0.
∴ `(3k + 2)((-1)/2)^3 + (k - 1) = 0`
`\implies (3k + 2)((-1)/8) + (k - 1) = 0`
`\implies (-(3k + 2))/8 + (k - 1) = 0`
`\implies (-3k - 2 + 8k - 8)/ 8 = 0`
⇒ (−3k − 2 + 8k − 8) = 0 × 8
⇒ 5k – 10 = 0
⇒ 5k = 10
⇒ k = `10/5`
⇒ k = 2
APPEARS IN
RELATED QUESTIONS
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Use the factor theorem to determine that x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1.
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
