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
Identify polynomials in the following:
`f(x)=4x^3-x^2-3x+7`
x4 − 7x3 + 9x2 + 7x − 10
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
Write the remainder when the polynomialf(x) = x3 + x2 − 3x + 2 is divided by x + 1.
If x − a is a factor of x3 −3x2a + 2a2x + b, then the value of b is
If x140 + 2x151 + k is divisible by x + 1, then the value of k is
If x + 2 is a factor of x2 + mx + 14, then m =
If x + 1 is a factor of the polynomial 2x2 + kx, then k =
Factorise the following:
(a + b)2 + 9(a + b) + 18
Factorise:
3x3 – x2 – 3x + 1
