Question

Find the zeroes of the quadratic polynomial 6x² - 3 - 7x and verify the relationship between the zeroes and the coefficients.

Answer 1

6x² – 7x – 3 = 0 ⇒ 6x² – 9x + 2x – 3 = 0 

⇒ 3x(2x – 3) + 1(2x – 3) = 0 ⇒ (2x – 3)(3x + 1) = 0 

⇒ 2x – 3 = 0 & 3x + 1 = 0 

x = 3/2 & x = -1/3 Hence, the zeros of the quadratic polynomials are 3/2 and -1/3.

For verification

Sum of zeros = - coefficient of x / coefficient of x² ⇒ 3/2 + (-1/3) = – (-7) / 6 ⇒ 7/6 = 7/6

Product of roots = constant / coefficient of x²  ⇒ 3/2 x (-1/3) = (-3) / 6 ⇒ -1/2 = -1/2

Therefore, the relationship between zeros and their coefficients is verified.