1. Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients

1 thought on “1. Find the zeroes of the following quadratic polynomials and verify the relationship between<br />the zeroes and the coefficients”

1. Answer:

   Given

   f(x) = 6×2 – 7x – 3

   To find the zeros

   Let us put f(x) = 0

   ⇒ 6×2 – 7x – 3 = 0

   ⇒ 6×2 – 9x + 2x – 3 = 0

   ⇒ 3x(2x – 3) + 1(2x – 3) = 0

   ⇒ (2x – 3)(3x + 1) = 0

   ⇒ 2x – 3 = 0

   x = 3/2

   ⇒ 3x + 1 = 0

   ⇒ x = -1/3

   It gives us 2 zeros, for x = 3/2 and x = -1/3

   Hence, the zeros of the quadratic equation are 3/2 and -1/3.

   Now, 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.

   Reply