Question

# If $α,β$ are the zeros of the polynomial $f(x)=x_{2}−p(x+1)−c=0$ such $(α+1)(β+1)=0$, then $c=$

**A**

## $1$

**B**

## $0$

**C**

## $−1$

**D**

## $2$

Medium

Solution

Verified by GMS

Correct option is A)

Question

Medium

Solution

Verified by GMS

Correct option is A)

$f(x)=x_{2}−p(x+1)−c=0$

$f(x)=x_{2}−px−(p+c)=0$ .............$(1)$

Since,

$α,β$ are the zeroes of the above polynomial.

So,

$α+β=p$

$αβ=−(p+c)$

Since,

$(α+1)(β+1)=0$

$αβ+α+β+1=0$

$−p−c+p+1=0$

$−c+1=0$

$c=1$

Hence, this is the answer.

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