Question 28

# Given the quadratic equation $$x^2 - (A - 3)x - (A - 2)$$, for what value of $$A$$ will the sum of the squares of the roots be zero?

Solution

For summation of square of roots to be zero, individual roots should be zero.
Hence summation should be zero i.e.  A-3=0 ; A = 3
And product of roots will also be zero i.e. A-2 = 0 ; A =2
So there is no unique value of A which can satisfy above equation.