Question

Find the zeros of f into x is equal to a b x square + b square minus A C into x minus b c and verify its relationship between zeroes and coefficients

Answer 1

f(x) = abx² + (b²-ac)x - bc      = abx² + b²x - acx - bc      = abx² - acx + b²x - bc      = ax(bx-c) + b(bx-c)      = (ax + b)(bx - c)α = -b/aβ = c/b
verification,by sumα + β = -(b²+ac)/ab-b/a + c/b = -b² - ac/ab-b²-ac/ab = -b²-ac/abLHS=RHS
by product αβ = -bc/ab-b/a X c/b = -c/a-c/a = -c/aLHS=RHSHence, verified