Advertisements
Advertisements
प्रश्न
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
Advertisements
उत्तर
Let f(x) = x3 + ax2 − 2x +a + 4 be the given polynomial.
By the factor theorem, (+ a) is the factor of f(x), if f(− a) = 0, i.e.,
`f(-a) = (-a)^3 + a(-a)^2 -2(-a) + a + 4 = 0`
`-a^3 + a^3 2a + a + 4 = 0`
`3a + 4 = 0`
`a = (-4)/3`
Thus, the value of a is − 4/3.
APPEARS IN
संबंधित प्रश्न
Identify polynomials in the following:
`g(x)=2x^3-3x^2+sqrtx-1`
If the polynomials ax3 + 3x2 − 13 and 2x3 − 5x + a, when divided by (x − 2) leave the same remainder, find the value of a.
f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
Find the value k if x − 3 is a factor of k2x3 − kx2 + 3kx − k.
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
x3 − 2x2 − x + 2
Factorise the following:
a2 + 10a – 600
Which of the following has x – 1 as a factor?
Factorise:
3x3 – x2 – 3x + 1
