Find the zeros of the Polynomial 6x² – 3 – 7x and Verify the Relationship between the zeros and the Coefficients of the Polynomial

Answer:

f(x) = 6x² – 7x – 3

To find the 0:

Let us put f(x) = 0

6x²– 7x – 3 = 0

⇒ 6x²– 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

For x = 3/2 and x = -1/3, it gives us two zeros.

As a result, the quadratic equation’s zeros are 3/2 and -1/3.

Now it’s time for verification.

− coefficient of x / coefficient of x2 = sum of zeros

3/2 + (-1/3) = – (-7) / 6 7/6 = 7/6

Roots product = constant / x2 coefficient

3/2 x (-1/3) = (-3) / 6 -1/2 = -1/2

As a result, the connection involving zeros and their coefficients has been established.