Question

If a and B are zeroes of p(x) =x²-p(x+1)+c such that ( a+1) (B+1) =0 then find 'C'

Answer 1

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star ANSWER ::}}}\mid}}}\end{gathered}$

Given :-

• a and B are zeroes of p(x) =x² - p (x+1) + c.
• (a+1) (b+1) =0

To Find :-

• The value of 'c' .

Solution :-

It is given that (a+1) (b+1) =0

Therefore, (a+1) = 0 or (b+1) = 0

(a+1) = 0 or (b+1) = 0

a = -1 or b = -1

Since,

α,β are the zeroes of the above polynomial.

So,

α+β = p

αβ = − (p+c)

Since,

(α+1)(β+1)=0

αβ + α + β + 1 = 0

− p −c +p +1 = 0

−c +1 = 0

$\star \: \underline{\large \boxed{c = 1}} \: \star$

@SweetestBitter