Question

find the zeroes of the polynomial 15+p(7-2p) and verify the relation between zeroes and coefficients

Answer 1

Let p(x)= 15+p(7-2p)= 15+7p -2p^2 = -2p^2 +7p +15 .

For the zeros of the given polynomial ,

-2p^2 +7p +15=0

-2p^2 +10p -3p +15=0

-2p(p-5)-3(p-5)=0

(-2p-3)(p-5)=0

-1(2p+3) (p-5)=0

(2p +3 ) (p-5)=0

→2p+3 = 0 or , p-5 =0

Thus , p=-3/2 or , 5 are the zeros of the given polynomial

p(x).

Verification ,

Sum of zeros = (-3/2+5)=( -3+10)/2= 7/2 = -(7/-2)= -(coefficient of p)/coefficient of p^2 .

Product of zeros =-(3/2×5)=-15/2= (15/-2)=( constant term )/(coefficient of p^2)

Answer 2

hope it helps u........☺☺