Question

15. Ifaand ß are the zeros of the quadratic polynomial f(x)= x2 - p(x + 1) – C, show that
(a+1)(B+ 1) = 1 - c​

Answer 1

Ifaand ß are the zeros of the quadratic polynomial f(x)= x2 - p(x + 1) – C, show that

(a+1)(B+ 1) = 1 - c

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Answer 2

Step-by-step explanation:

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Here is your answer↓

it is given that

f (x)=x²-px-p-c

=x²-px-(p+c)

By comparing quadratic equation ax²+bx+c

a=1; b=-p; c=-(p+c)

we know that

œ+ß=-b/a

=-(-p)/1 =-p

ϧ=c/a

=-(p+c)/1 =-(p+c)

A/Q,

L.H.S:-

=(œ+1)(ß+1)

=(œß)+(œ+ß)+1

Put the value of œ+ß and œß.

= -(p+c)+(-p)+1

= -p-c-p+1

= 1-c.

R.H.S :- 1-c.

Hence, it is proved L.H.S=R.H.S