Math, asked by BrainlyHelper, 1 year ago

If  \alpha \beta are the zeros of the polynomial  f(x)=x^{2}-p(x+1)-c, such that  (\alpha +1)(\beta +1) = 0 then c =
(a) 1
(b) 0
(c) -1
(d) 2

Answers

Answered by nikitasingh79
1

SOLUTION :

The correct option is (a) : 1 .

Given : α  and β are the zeroes of the  polynomial f(x) = x² -  p(x + 1) - c

f(x) = x² -  px - p - c

On comparing with ax² + bx + c,

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

Sum of the zeroes = −coefficient of x / coefficient of x²

α + β  = -b/a = - (- p)/1  

α + β  =  p ………………….(1)

Product of the zeroes = constant term/ Coefficient of x²

αβ = c/a = - p - c/1  

αβ = - p - c  ……………………(2)

Given : (α + 1)  (β + 1) = 0

0 = αβ + β + α + 1

0 = αβ + (α + β )+ 1

0 = - p - c + p + 1

[From eq 1 & 2 ]

0 = - p + p - c + 1

0 = - c + 1

c = 1  

Hence, the value of c is 1 .

HOPE THIS ANSWER WILL HELP YOU..

Answered by shikha2019
3
The correct option is (a). 1
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