Find the quadratic polynomial whose zeroes are 2/3 and -1/4. Verify th

1.	Find the quadratic polynomial whose zeroes are 2/3 and -1/4. Verify the relation between the coefficients and the zeroes of the polynomial.
Answer» Let ∝ = 2/3 and β = -1/4 Sum of the zeroes = (∝ + β) = 2/3 + -1/4 = 5/12 Product of the zeroes, = 2/3 x -1/4 = -1/6 Required quadratic polynomial is x² – (∝+β)x + ∝β = x² – (5/12)x – (-1/6) = 1/12(12x² – 5x – 2) And, Sum of the zeroes = 5/12 = (-Coefficient of x)/(Cofficient of x²) Product of zeroes = -1/6 = Constant term / Coefficient of x²

Find the quadratic polynomial whose zeroes are 2/3 and -1/4. Verify the relation between the coefficients and the zeroes of the polynomial.

Answer»

Let ∝ = 2/3 and β = -1/4

Sum of the zeroes = (∝ + β) = 2/3 + -1/4 = 5/12

Product of the zeroes, = 2/3 x -1/4 = -1/6

Required quadratic polynomial is

x² – (∝+β)x + ∝β

= x² – (5/12)x – (-1/6)

= 1/12(12x² – 5x – 2)

And,

Sum of the zeroes = 5/12 = (-Coefficient of x)/(Cofficient of x²)

Product of zeroes = -1/6 = Constant term / Coefficient of x²