Question

Find
the zeroes of the quadratic
polynomial 6x² + x-2 and verify
The relationship between the Zeroes
and the coefficients.​

Answer 1

Answer:

$6 {x}^{2} + x - 2 = 0 \\ \\ 6 {x}^{2} + 4x - 3x - 2 = 0 \\ \\ 2x(3x + 2) - 1(3x + 2) = 0 \\ \\ (3x + 2) \: \: (2x - 1) = 0$

If 3x + 2 = 0

$3x = - 2 \\ \\ x = \frac{ - 2}{3}$

If 2x - 1 = 0

$2x = 1 \\ \\ x = \frac{1}{2}$

Now,

$sum \: of \: zeroes( \alpha + \beta ) = \frac{ -2 }{3} + \frac{1}{2} \\ \\ = \frac{ - 4 + 3}{ 6} \\ \\ = \frac{ - 1}{6} = \frac{ - b}{a}$

$product \: of \: zeroes( \alpha \beta ) = \frac{ - 2}{3} \times \frac{1}{2} \\ \\ = \frac{ - 1}{3} = \frac{c}{a}$

If you satisfied mark it brainliest.