Question

If & and B are the zeroes of the
quad polynomial f(x) = x²
- p(x +1)-&, show that
(a +1) ( beta + 1 ) = 1-c​

Answer 1

•Qᴜᴇsᴛɪᴏɴ↓:-

If & and B are the zeroes of the

quad polynomial f(x) = x²

- p(x +1)-&,show that

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

•Gɪᴠᴇɴ:-

& and B are the zeroes of the

quad polynomial f(x) = x²

- p(x +1)-&

•Sʜᴏᴡ ᴛʜᴀᴛ:-

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

•Sᴏʟᴜᴛɪᴏɴ:-

If alpha and Beta are the zeroes of the polynomial x^2-p(x+1)-c, find the value of (alpha +1)(beta+1)

Asked by Nimmi | 7th May, 2019, 11:36: PM

Expert Answer:

If alpha and Beta are the zeroes of the polynomial x^2-p(x+1)-c, find the value of (alpha +1)(beta+1)

x2 - p(x + 1) - c

= x2 - px - p - c

Comparing with ax2 + bx + c, we get

a= 1 , b = -p and c = - p - c

α and β are the zeroes of the given polynomial.

→ α + β = -b/a = -(-p)/1 = p

and αβ = c/a = -p - c / 1 = -p - c

To find: (α + 1)(β + 1)

(α + 1)(β + 1) = αβ + α + β + 1

= - p - c + p + 1

= 1 - c

Answer 2

$hence \: proved$