Question 2 (ii)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
√2,13
√2,13
Let the polynomial be ax2+bx+c, and its zeroes be α and β.
α+β=√2.
αβ=13=ca
∴ α+β = 3√23=−ba
∴ a = 3, b = -3√2, c = 1
∴ Quadratic polynomial is 3x2−3√2x+1.