Question

if alpha and beta are zeros of x2-ax+a find the value of -1/alpha 3+1/beta 3

Answer 1

Now we know that

sum of the roots==-b/a=alpha+beta=-(-a)/1=a

now product of roots=c/a=alpha(beta)=a

now -1/3alpha+1/3beta

-3beta+3alpha/9(alpha)(beta)

-3(alpha-a)+3alpha/9alpha. beta

since{alpha+beta=a

alpha-a=-beta}

-3alpha+3a+3alpha/9alpha beta

3a/9(a)

3a/9a

=1/3

so now -1/3alpha+1/3beta=1/3