Advertisements
Advertisements
प्रश्न
In the following two polynomials, find the value of ‘a’ if x – a is a factor of each of the two:
x5 - a2x3 + 2x + a + 1.
Advertisements
उत्तर
Let p(x) = x5 - a2x3 + 2x + a + 1
Since (x -a) in a factor of p(x), so p(a) = 0.
Put x = a in equation (i) we get
p(a) = (a)5 - a2 (a)3 + 2a + a + 1 = 0
= a5 - a2 x a3 + 3a + 1 = 0
= a5 - a5 + 3a + 1 = 0
= 3a + 1 = 0
⇒ 3a = -1
⇒ a = `-(1)/(3)`.
संबंधित प्रश्न
The expression 4x3 – bx2 + x – c leaves remainders 0 and 30 when divided by x + 1 and 2x – 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the values of p and q. Also, for these values of p and q, factorize the given polynomial completely.
Find the value of a and b so that the polynomial x3 - ax2 - 13x + b has (x - 1) (x + 3) as factor.
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x3 + ax2 − 2x + a + 4
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
The polynomial 3x3 + 8x2 – 15x + k has (x – 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.
If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
