Question

if alpha and beta are two zeroes of polynomial x²-3x-2 .then find the value of alpha and beta.

Answer 1

Hey user

Here is your answer :-

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x^2 - 3x - 2 = 0

$d = {b}^{2} - 4ac \\ \\ = {( - 3)}^{2} - 4(1)( - 2) \\ \\ = 9 + 8 \\ \\ = 17 \\ \\ \alpha = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ = \frac{ - ( - 3) + \sqrt{17} }{2} \\ \\ = \frac{3 + \sqrt{17} }{2} \\ \\ \beta = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ = \frac{ - ( - 3) - \sqrt{17} }{2} \\ \\ = \frac{3 - \sqrt{17} }{2}$