Question

If alpha and beta are the root of quadratic equation 2 x square minus x minus 1 is equal to zero find alpha and beta

Answer 1

Answer:

$\alpha = \frac{ - 1}{2} \\ \\ \beta = 1$

Step-by-step explanation:

If

$\alpha \: and \: \beta$

are the roots of Quadratic equation

$2 {x}^{2} - x - 1 = 0$

The relation of roots and coefficient of polynomial is given by,if the standard Quadratic equation is

$a {x}^{2} + bx + c = 0 \\ \\ \alpha + \beta = \frac{ - b}{a} \\ \\ \alpha \beta = \frac{c}{a}$

Here

$a = 2 \\ \\ b = - 1 \\ \\ c = - 1 \\ \\ \alpha + \beta = \frac{1}{2} ...eq1 \\ \\ \alpha \beta = \frac{ - 1}{2}...eq2$

$2 {x}^{2} - x - 1 = 0 \\ \\ 2 {x}^{2} - 2x + x - 1 = 0 \\ \\ 2x(x - 1) + 1(x - 1) = 0 \\ \\ (2x + 1)(x - 1) = 0 \\ \\ x - 1 = 0 \\ \\ x = 1 \\ \\ 2x + 1 = 0 \\ \\ x = \frac{ - 1}{2}$

so

$\alpha = \frac{ - 1}{2} \\ \\ \beta = 1$

We can interchange the values also.

Also you can verify the values.

Hope it helps you.