Question

Find the zeroes of the quadratic polynomial 4x² - 6 - 8x and verify the
relationship between the zeroes and the coefficients of the
polynomial.​

Answer 1

Step-by-step explanation:

4x² -8x -6

$\alpha + \beta = \frac{ - 8}{4}$

$\alpha = - 2 - \beta$

$\alpha \beta = \frac{ - 6}{4}$

$- 2 \beta - { \beta }^{2} = \frac{ - 3}{2}$

$- 4 \beta - 4 { \beta }^{2} = - 3$

$4 { \beta }^{2} + 4 \beta - 3 = 0$

$4 { \beta }^{2} + 6 \beta - 2 \beta - 3 \\ = 2 \beta (2 \beta + 3) - 1(2 \beta + 3) \\ = \beta = \frac{1}{2} and \frac{ - 3}{2}$