Question

P(x)=2x³-3px²+px+q have x-1 as a factor and have -52 as reminder when divide by x-2..
What value of p and q?

Answer 1

Answer:p=29/4

q=25/2

Step-by-step explanation:

p(x)=2x²-3px²+px+q

x-1 is factor

then

p(1)=2x²-3px²+px+q=0

⇒2(1)²-3p(1)+p(1)+q=0

⇒2-3p+p+q=0

⇒-2p+q= -2

⇒2p-q=2  .....eq1

p(2)=2x²-3px²+px+q=-52

⇒2(2)²-3p(2)²+(2)p+q= -52

⇒8-12p+2p+q= -52

⇒-10p+q=-60  .....eq2

add eq1 and eq2

-10p+q+2p-q= -60+2

-8p=-58

p=29/4

put p=29/4

-10p+q=-60

-10(29/4)+q= -60

-145/2+q=-60

q= 145/2-60

q=(145-120)/2

q=25/2