Advertisements
Advertisements
Question
Find the value k if x − 3 is a factor of k2x3 − kx2 + 3kx − k.
Advertisements
Solution
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
RELATED QUESTIONS
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`f(x)=0`
Find the integral roots of the polynomial f(x) = x3 + 6x2 + 11x + 6.
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
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
If both x + 1 and x − 1 are factors of ax3 + x2 − 2x + b, find the values of a and b.
y3 − 2y2 − 29y − 42
2y3 + y2 − 2y − 1
2x4 − 7x3 − 13x2 + 63x − 45
Factorise the following:
12x2 + 36x2y + 27y2x2
(x + y)(x2 – xy + y2) is equal to
