Question

Find the zeroes of the quadratic polynomial 2x² - 4x - 6 and verify the relationship between the zeroes and the coefficients​

Answer 1

Step-by-step explanation:

just take out the zeroes and verify them using the sum of zeroes and product of zeroes formula

Answer 2

$there \: are \: 2 \: formula \: which \: shows \: relationship \: between \: the \: zeroes \: and \: the \: coefficients$

$x = \frac{ - b + \sqrt{ {b }^{2} - 4ac } }{2a} \: or \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a}$

${x }^{2} - ( \alpha + \beta )x + \alpha \beta=0$

$x = \frac{4 + \sqrt{ { - 4}^{2} - 4 \times 2 \times - 6 } }{4} or \frac{4 - \sqrt{ { - 4}^{2} - 4 \times 2 \times - 6 } }{4}$

$x = \frac{4 + \sqrt{64} }{4} \: or \: \frac{4 - \sqrt{64} }{4}$

$x = \frac{4 + 8}{4} \: or \: \frac{4 - 8}{4}$

$x = \frac{12}{4} \: or \: \frac{ - 4}{4}$

$x = 3 \: or \: - 1$

$here$

$\alpha = 3 \: and \: \beta = - 1$

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

${x}^{2} - 2x + - 3=0$

Multiple this equation by 2

2x²-4x-6=0