if alpha,beta are zero of the quadratic polynomial p(x)=x2-p (x+1)-c find the value of (alpha+1) (beta+1) =1-C.
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10th
Maths
Polynomials
Relationship between Zeroes and Coefficients of a Polynomial
If alpha, beta are the zero...
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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=
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We have,
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
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