Advertisements
Advertisements
प्रश्न
In the following two polynomials, find the value of a, if x + a is a factor x4 − a2x2 + 3x −a.
उत्तर
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
संबंधित प्रश्न
f(x) = x4 − 3x2 + 4, g(x) = x − 2
f(x) = x3 − 6x2 + 11x − 6, g(x) = x2 − 3x + 2
Find the value k if x − 3 is a factor of k2x3 − kx2 + 3kx − k.
What must be subtracted from x3 − 6x2 − 15x + 80 so that the result is exactly divisible by x2 + x − 12?
x3 − 6x2 + 3x + 10
x3 − 10x2 − 53x − 42
2y3 − 5y2 − 19y + 42
Mark the correct alternative in each of the following:
If x − 2 is a factor of x2 + 3ax − 2a, then a =
Factorise the following:
t² + 72 – 17t
Factorise the following:
12x2 + 36x2y + 27y2x2
