Question

If a polynomial 3x^4-15x^3+14x^2+px-q is divisible by x^2-5x +6,then find the value of p and q

Answer 1

See the photo attached

The value of p=20 and q=24

The remainders are compated to zero

Answer 2

Step by step Explanation :-

ANSWER

3x

4

−15x

3

+14x

2

+2px−q is divisible by x

2

−5x+16 i.e. (x−2)(x−3)

∴ x=2 & x=3, are the zeroes of polynomial

So, at x=2 & x=3 , the value of polynomial is zero.

∴3(2)

4

−15(2)

3

+14(2)

2

+2p(2)−q=0

⇒48−120+56+4p−q=0

⇒4p−q=16⟶(1)

& 3(3)

4

−15(3)

3

+14(3)

2

+2p(3)−q

⇒243−405+126+6p−q=0

⇒6p−q=36⟶(2)

Solving both equ (1) & equ(2)

2p=20⇒p=

10

& q=4(10)−16=

24

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