Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let p(x) = x5 - 3x4 - ax3 + 3ax2 + 2ax + 4 ...(i)
Since, (x - 2) is facxtor of p(x), so p(2) = 0
Put x = 2 in equation (i) we get
p(2) = (2)5 - 3(2)4 -a(2)3 + 3a(2)2 + 2a(2) + 4
= 32 - 3 x 16 - a x 8 + 3a x 4 + 4a + 4
= 32 - 48 - 8a + 12a + 4a + 4
= 8a - 12
But p(2) = 0
⇒ 8a = 12 = 0
⇒ a = `(12)/(8)`
⇒ a = `(3)/(2)`.
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’.
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.
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.
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
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x4 - a2x2 + 3x - a.
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
Use factor theorem to factorise the following polynomials completely: x3 – 19x – 30
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is ______.
