Advertisements
Advertisements
Question
If x − 2 is a factor of the following two polynomials, find the values of a in each case x3 − 2ax2 + ax − 1.
Advertisements
Solution
Let `f(x) = x^3 - 2ax^2 + ax - 1` be the given polynomial.
By factor theorem, if (x − 2) is a factor of f(x), then f (2) = 0
Therefore,
`f(2) = (2)^3 - 2a(2)^2 a(2) - 1 = 0`
`8-8a + 2a - 1 = 0`
`-6a + 7 = 0`
`a = 7/6`
Thus the value of a is 7/6.
APPEARS IN
RELATED QUESTIONS
Identify polynomials in the following:
`f(x)=2+3/x+4x`
If x = 0 and x = −1 are the roots of the polynomial f(x) =2x3 − 3x2 + ax + b, find the value of a and b.
f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
If x + 1 is a factor of x3 + a, then write the value of a.
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 =
Let f(x) be a polynomial such that \[f\left( - \frac{1}{2} \right)\] = 0, then a factor of f(x) is
Factorise the following:
2a2 + 9a + 10
