Find the zeros of the quadratic polynomials 2x2 – 11x + 15 and ver

1.	Find the zeros of the quadratic polynomials 2x2 – 11x + 15 and verify the relationship between the zeros and the coefficients.
Answer» Let f(x) = 2x² ˗ 11x + 15 = 2x² ˗ (6x + 5x) + 15 = 2x² ˗ 6x ˗ 5x + 15 = 2x (x ˗ 3) ˗ 5 (x ˗ 3) = (2x ˗ 5) (x ˗ 3) To find the zeroes, set f(x) = 0 (2x ˗ 5) (x ˗ 3) = 0 2x ˗ 5= 0 or x ˗ 3 = 0 x = 5/2 or x = 3 Again, Sum of zeroes = 5/2 + 3 = (5+6)/2 = 11/2 = -b/a = (-Coefficient of x)/(Cofficient of x²) Product of zeroes = 5/2 x 3 = 15/2 = c/a = Constant term / Coefficient of x²

Find the zeros of the quadratic polynomials 2x2 – 11x + 15 and verify the relationship between the zeros and the coefficients.

Answer»

Let f(x) = 2x² ˗ 11x + 15

= 2x² ˗ (6x + 5x) + 15

= 2x² ˗ 6x ˗ 5x + 15

= 2x (x ˗ 3) ˗ 5 (x ˗ 3)

= (2x ˗ 5) (x ˗ 3)

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

(2x ˗ 5) (x ˗ 3) = 0

2x ˗ 5= 0 or x ˗ 3 = 0

x = 5/2 or x = 3

Again,

Sum of zeroes = 5/2 + 3 = (5+6)/2 = 11/2

= -b/a

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

Product of zeroes = 5/2 x 3 = 15/2

= c/a

= Constant term / Coefficient of x²