Advertisements
Advertisements
प्रश्न
Find the value k if x − 3 is a factor of k2x3 − kx2 + 3kx − k.
उत्तर
Let `f(x) = k^2 x^3 - kx^2 + 3kx - k` be the given polynomial.
By the factor theorem,
(x − 3) is a factor of f(x) if f (3) = 0
Therefore,
`f(3) = k^2 (3)^3 - k(3)^2 + 3k(3) - k = 0`
\[\Rightarrow 27 k^2 - 9k + 9k - k = 0\]
\[ \Rightarrow 27 k^2 - k = 0\]
\[ \Rightarrow k\left( 27k - 1 \right) = 0\]
\[ \Rightarrow k = 0 \text { or k } = \frac{1}{27}\]
Hence, the value of k is 0 or `1/27`.
APPEARS IN
संबंधित प्रश्न
Write the degrees of the following polynomials:
`5y-sqrt2`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`f(x)=0`
Find rational roots of the polynomial f(x) = 2x3 + x2 − 7x − 6.
f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7)
f(x) = x3 − 6x2 + 11x − 6; g(x) = x − 3
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
If f(x) = x4 − 2x3 + 3x2 − ax − b when divided by x − 1, the remainder is 6, then find the value of a + b
If x − 3 is a factor of x2 − ax − 15, then a =
Factorise the following:
8m3 – 2m2n – 15mn2
