Question

Find the zeroes of the polynomial \(2x^2 + 7x + 5\) and verify the relationship between its zeroes and coefficients.

Hint:

To verify relationships, use sum \(= -\dfrac{b}{a},\) product \(= \dfrac{c}{a}\) from standard quadratic form.

Answer 1

Given: \(2x^2 + 7x + 5\) Factor: \[ 2x^2 + 7x + 5 = 2x^2 + 2x + 5x + 5 = 2x(x + 1) + 5(x + 1) = (x + 1)(2x + 5) \Rightarrow x = -1,\ -\dfrac{5}{2} \] Verify: \[ \text{Sum of roots} = -1 - \dfrac{5}{2} = -\dfrac{7}{2} = \dfrac{-b}{a} = \dfrac{-7}{2} \] \[ \text{Product} = (-1) \cdot (-\dfrac{5}{2}) = \dfrac{5}{2} = \dfrac{c}{a} = \dfrac{5}{2} \]