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 constant, linear, quadratic and cubic polynomials from the following polynomials:
`h(x)=-3x+1/2`
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
What must be added to 3x3 + x2 − 22x + 9 so that the result is exactly divisible by 3x2 + 7x − 6?
One factor of x4 + x2 − 20 is x2 + 5. The other factor is
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
Factorise the following:
a4 – 3a2 + 2
