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.
If (x - 2) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
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
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
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.
For what value of k is the polynomial p(x) = 2x3 – kx2 + 3x + 10 exactly divisible by (x – 2)
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 ______.
Factors of 3x3 – 2x2 – 8x are ______.
