Advertisements
Advertisements
प्रश्न
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’.
Advertisements
उत्तर
If (x – 3) divides f(x) = x3 – px2 + x + 6, then
Remainder = f(3) = 33 – p(3)2 + 3 + 6 = 36 – 9p
If (x−3) divides g(x) = 2x3 – x2 − (p + 3)x – 6, then
Remainder = g(3) = 3(3)3 – 32 − (p + 3)(3) – 6 = 30 - 3p
Now f(3) = g(3)
⇒ 36 – 9p = 30 − 3p
⇒ −6p = −6
⇒ p = 1
APPEARS IN
संबंधित प्रश्न
Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the 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:
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: 4x3 + 4x2 – 9x – 9
f 2x3 + ax2 – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorize the given expression.
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 ______.
