Advertisements
Advertisements
प्रश्न
Find the values of p and q in the polynomial f(x)= x3 - px2 + 14x -q, if it is exactly divisible by (x-1) and (x-2).
Advertisements
उत्तर
(x - 1) ⇒ x = l .... (i)
(x - 2) ⇒ x = 2 .... (ii)
Putting (i) in polynomial , we get
f(l) = 1× 1 × 1 - p × 1 × 1 + 14 × 1 - q = 0
⇒ p + q = 15
⇒ p = 15 - q
Putting (ii) in polynomial , we get
f(2) = 2 × 2 × 2 - p × 2 × 2 + 14 × 2 - q = 0
4p + q= 36, ⇒ q = 36 - 4p .... (iv)
Combining (iii) and (iv), we get,
p = 15 - (36 - 4p)
⇒ p= 15 - 36 + 4p
⇒ 3p = 21
q = 36 - 4 × 7 = 8
⇒ p = 7 , q = 8
APPEARS IN
संबंधित प्रश्न
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Find the remainder when x4 + 1 is divided by x + 1.
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 2x2 – 5x + 1
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
