Advertisements
Advertisements
Question
In the following two polynomials, find the value of a, if x + a is a factor x4 − a2x2 + 3x −a.
Advertisements
Solution
Let `f(x) = x^4 - a^2x^2 + 3x - a ` be the polynomial. By factor theorem, (x + a) is a factor of the f(x), if f(− a) = 0, i.e.,
`f(-a) = (-a)^4 - a^2 (-a)^2 + 3(-a)-a = 0`
`a^4 - a^4 - 3a - a = 0`
-4a = 0
`a = 0`
Thus, the value of a is 0.
APPEARS IN
RELATED QUESTIONS
Write the coefficient of x2 in the following:
`sqrt3x-7`
Identify polynomials in the following:
`g(x)=2x^3-3x^2+sqrtx-1`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`h(x)=-3x+1/2`
Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:
\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
x3 − 6x2 + 3x + 10
x3 − 23x2 + 142x − 120
x4 + 10x3 + 35x2 + 50x + 24
Factorise the following:
8m3 – 2m2n – 15mn2
