Advertisements
Advertisements
प्रश्न
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is ______.
विकल्प
– 6
12
6
–12
Advertisements
उत्तर
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is 6.
Explanation:
Let f(x) = x3 – kx2 + 11x – 6
Since x – 1 is a factor of f(x)
∴ f(1) = 0
`\implies` 13 – k · 12 + 11 – 6 = 0
`\implies` 1 – k + 11 – 6 = 0
`\implies` 6 – k = 0
`\implies` k = 6
APPEARS IN
संबंधित प्रश्न
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the polynomial completely.
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x4 - a2x2 + 3x - a.
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x5 - 3x4 - ax3 + 3ax2 + 2ax + 4.
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
If x3 – 2x2 + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorize the given polynomial completely.
If (x + 3) and (x – 4) are factors of x3 + ax2 – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.
