If are the zeros of the polynomial such that = 0 then c =
(a) 1
(b) 0
(c) -1
(d) 2
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Answered by
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 .
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Answered by
3
The correct option is (a). 1
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