Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence, find the zeros of the polynomial
Let the zero of the polynomial be α and β
According to the question,
α + β = 8
αβ = 12
∴f(x)= x2 – (α + β)x + (αβ)
=x2 - 8x + 12
∴required polynomial f(x) = x2 - 8x + 12
Put f(x) = 0
x2 - 8x + 12 = 0
x2 - 6x -2x + 12 = 0
x(x – 6) -2(x – 6) = 0
(x - 6)(x - 2)=0
x = 6 or x = 2