Question

Find the zeros of the quadratic polynomial 3x^+5x-2 and verify the relationship between zeros and coefficients​

Answer 1

Step-by-step explanation:

$3 {x}^{2} + 5x - 2 \\ 3 {x}^{2} + 6x - x - 2 \\ 3x(x + 2) - 1(x + 2) \\ (3x - 1)(x + 2) \\ x = \frac{1}{3} \: or \: x = - 2$

$\alpha + \beta = \frac{ - b}{a} \\ \frac{1}{3} - 2 = \frac{ - 5}{3 } \\ \frac{1 - 6}{3} = \frac{ - 5}{3} \\ \frac{ - 5}{3} = \frac{ - 5}{3}$

$\alpha \beta = \frac{c}{a} \\ \frac{1}{3} \times - 2 = \frac{ - 2}{3} \\ \frac{ - 2}{3} = \frac{ - 2}{3}$

Hence verified