Advertisements
Advertisements
प्रश्न
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
Advertisements
उत्तर
Let p(x) = x2 - 3x + 5a ...(i)
Since, (x - 2) is a factor of p(x), so p(2) = 0 ...(by factor theorem)
Put x = 2 in equation (i), we get
p(2) = (2)2 - 3 x 2 + 5a
= 4 - 6 + 5a
= 5a - 2
But p(2) = 0
⇒ 5a -2 = 0
⇒ 5a = 2
⇒ a = `(2)/(5)`.
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’.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
If (x + 1) and (x – 2) are factors of x3 + (a + 1)x2 – (b – 2)x – 6, find the values of a and b. And then, factorise the given expression completely.
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
Find the value of a and b so that the polynomial x3 - ax2 - 13x + b has (x - 1) (x + 3) as factor.
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.
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
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.
