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
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
Factorise the expression f(x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
In the following two polynomials, find the value of ‘a’ if x – a is a factor of each of the two:
x6 - ax5 + x4 - ax3 + 3a + 2
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x5 - 3x4 - ax3 + 3ax2 + 2ax + 4.
If x3 – 2x2 + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorize the given polynomial completely.
If (2x + 1) is a factor of both the expressions 2x2 – 5x + p and 2x2 + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is ______.
