Question

if 8, 2 are the roots of x square + ax + beta = 0 and 3,3 are the roots of x square + alpha x + b = 0 then the product of X square + ax+b=0 is

Answer 1

A2A.

Given that a and b are roots of the equation x^2 +ax +b=0,

we can apply the results for the sum and product of the roots.

Sum of roots= a+b = -a,

     Hence 2a+b=0.

Product of roots= ab = b,

Since if b becomes zero, both a and b will become zero. Hence in this case function will be f(x) = x^2. So it's minimum value will be 0.

If a and b are non-zero, from above equation a=1.

So b = -2.

Hence function is f(x) = x^2 +x -2.

Thus f'(x) = 2x+1=0, so x =-1/2.

Putting this in f(x),

f(-1/2) = 1/4 -1/2 -2 = -9/4.

So minimum value in this case will be -9/4.