Question

if alpha and beta are the zeroes of x2+px+q then find the value of ( 1/alpha - 1/beta)​

Answer 1

Answer:

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Answer 2

Given that alpha and beta are the roots of the quadratic equation  f(x) = x^2-p(x+1)-c = x^2-px-p-c = x^2 -px-(p+c),  

comparing with ax^2 + bx + c, we have, a =1 , b= -p & c= -(p+c)  

alpha+beta = -b/a = -(-p)/1 = p  

& alpha*beta = c/a = -(p+c)/1 = -(p+c)  

Therefore, (Alpha + 1)*(beta+1)  

= Alpha*beta + alpha + beta + 1  

= -(p+c) + p + 1  

= -p-c+p+1  

= 1-c

or c=1

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