If - and - are the zeroes of the polynomial f x - x 2- p x -1- c- then -1-1 is equal to-

As alpha and beta are the zeroes of the polynomial x2 p(x+1) c=x2 px p c the sum of zeroes, alpha+beta= (coefficient of x)/coefficient of x^2=–p/1=p product ...

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Standard X

Mathematics

Formation of a Quadratic Equation From It's Roots

If α and β ar...

Question

If α and β are the zeroes of the polynomial f(x)=x²-p(x+1)-c,then (α+1)(β+1) is equal to?

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Solution

as alpha and beta are the zeroes of the polynomial x²-p(x+1)-c=x²-px-p-c
the sum of zeroes, alpha+beta=-(coefficient of x)/coefficient of x^2=--p/1=p
product of zeroes alphabeta=coefficient of constant/coefficient of x^2=-p-c/1=-p-c
so
(α+1)(β+1)=αβ+α+β+1=(αβ)+(α+β)+1=-p-c+p+1=1-C

ok THANKS

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If α and β are the zeroes of the polynomial f(x)=x2 -p(x+1)-c,then (α+1)(β+1) is equal to?

If α and β are the zeroes of the polynomial f(x)=x²-p(x+1)-c,then (α+1)(β+1) is equal to?