Advertisements
Advertisements
प्रश्न
Find the value of a and b so that the polynomial x3 - ax2 - 13x + b has (x - 1) (x + 3) as factor.
Advertisements
उत्तर
Let p(x) = x3 - ax2 - 13x + b be the given polynomial.
If (x - 1) and (x + 3) are the factors of p(x) then
p(1) = 0
and p(-3) = 0
p(1) = (1)3 - a(1)2 - 13(1) + b = 0
= 1 - a - 13 + b = 0
a - b = -12 ...(1)
p(-3) = (-3)3 - a(-3)2 - 13(-3) + b = 0
= -27 - 9a + 39 + b = 0
9a - b = 12 ...(2)
Solving (1) and (2) we get
a = 3
and b = 15.
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.
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 values of a and b in the polynomial f(x) = 2x3 + ax2 + bx + 10, if it is exactly divisible by (x+2) and (2x-1).
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.
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 2x3 – x2 + px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely
The polynomial 3x3 + 8x2 – 15x + k has (x – 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.
(x – 2) is a factor of ______.
For the polynomial x5 – x4 + x3 – 8x2 + 6x + 15, the maximum number of linear factors is ______.
