Question

Find the zeros of the polynomial 2x² + 3x − 2 and verify the relationship between the zeroes and the coefficients.

Answer 1

The given polynomial is 2x² + 3x − 2. To find the zeros of the given polynomial, let

2x² + 3x − 2 = 0

⇒ 2x² + 4x − x − 2 = 0

⇒ 2x (x + 2) − 1 (x + 2) = 0

⇒ (x + 2)(2x − 1) = 0

⇒ x = `-2, 1/2`

The zeros of the given polynomial are −2 and `1/2`.

Now, `- 2 + 1/2 = (-3)/2 = - "coefficients of x"/"coefficients of x"^2`

and `-2 xx 1/2 = -1 = "constant term"/"coefficient of x"^2`