Question

If a and b are zeroes of the polynomial x^2-x -6, find a quadratic polynomial whose zeroes are (3a+2b) and (2a+3b)

Answer 1

As we know quadratic equation have only two solutions

Therefore,
p(x)=(3a+2b)(2a+3b)
=6a^2+9ab+4ab+6b^2
=6a^2+13ab+6b^2