Advertisements
Advertisements
Question
If x + a is a factor of x4 − a2x2 + 3x − 6a, then a =
Options
0
-1
1
2
Advertisements
Solution
As (x +a) is a factor of polynomial f(x) = x4 − a2x2 + 3x − 6a,
Therefore,
f(-a) = 0
`(-a)^4 - a^2 (-a)^2 +3(-a) - 6a = 0`
`a^4 - a^4 - 3a - 6a =0`
`a =0`
APPEARS IN
RELATED QUESTIONS
Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:
\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]
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.
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
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
Show that (x + 4) , (x − 3) and (x − 7) are factors of x3 − 6x2 − 19x + 84
If x3 + ax2 − bx+ 10 is divisible by x2 − 3x + 2, find the values of a and b.
Using factor theorem, factorize each of the following polynomials:
x3 + 6x2 + 11x + 6
Let f(x) be a polynomial such that \[f\left( - \frac{1}{2} \right)\] = 0, then a factor of f(x) is
If (3x − 1)7 = a7x7 + a6x6 + a5x5 +...+ a1x + a0, then a7 + a5 + ...+a1 + a0 =
If (x + 5) and (x – 3) are the factors of ax2 + bx + c, then values of a, b and c are
