Find the zeros of the quadratic polynomials 2√3 x2 – 5x + √3 a

1.	Find the zeros of the quadratic polynomials 2√3 x2 – 5x + √3 and verify the relationship between the zeros and the coefficients.
Answer» Let f(x) = 2 √3 x² – 5x + √3 = 2 √3 x² – 2x – 3x + √3 = 2x(√3x-1) – √3(√3x-1) To find the zeroes, set f(x) = 0 (√3x – 1) or (2x – √3) = 0 x = 1/√3 = √3/3 or x = √3/2 x = √3/3 or x = √3/2 Again, Sum of zeroes = √3/3 + √3/2 = 5√3/6 = -b/a = (-Coefficient of x)/(Cofficient of x²) Product of zeroes = √3/3 x √3/2 = √3/6 = c/a = Constant term / Coefficient of x²

Find the zeros of the quadratic polynomials 2√3 x2 – 5x + √3 and verify the relationship between the zeros and the coefficients.

Answer»

Let f(x) = 2 √3 x² – 5x + √3

= 2 √3 x² – 2x – 3x + √3

= 2x(√3x-1) – √3(√3x-1)

To find the zeroes, set f(x) = 0

(√3x – 1) or (2x – √3) = 0

x = 1/√3 = √3/3 or x = √3/2

x = √3/3 or x = √3/2

Again,

Sum of zeroes = √3/3 + √3/2 = 5√3/6

= -b/a

= (-Coefficient of x)/(Cofficient of x²)

Product of zeroes = √3/3 x √3/2 = √3/6

= c/a

= Constant term / Coefficient of x²