Advertisements
Advertisements
प्रश्न
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
Advertisements
उत्तर
Let `f(x) = x^5 - a^2 x^3 + 2x + a `+1 be the given polynomial.
By factor theorem, (x − a) is a factor of f(x), if f(a) = 0.
Therefore,
`⇒ f(a) = (a)^5 - a^2(a)^3 + 2 (a) + a + 1 = 0`
`a^5 - a^5 + 2a + a+1 = 0`
`3a + 1 = 0`
` a= (-1)/3`
Thus, the value of a is − 1/3.
APPEARS IN
संबंधित प्रश्न
f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1
f(x) = x4 − 3x2 + 4, g(x) = x − 2
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
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
Find the value k if x − 3 is a factor of k2x3 − kx2 + 3kx − k.
x3 + 13x2 + 32x + 20
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
If x + 1 is a factor of x3 + a, then write the value of a.
One factor of x4 + x2 − 20 is x2 + 5. The other factor is
Factorise:
3x3 – x2 – 3x + 1
