Advertisements
Advertisements
प्रश्न
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
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) = x3 − x2 − x − 1, q(x) = x − 1
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
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
Factors of 3x3 – 2x2 – 8x are ______.
