Question

if alpha and beta are the zeroes of the quadratic polynomial f(x) = x^2 + x -2 then find the value of alpha - beta

Answer 1

$\sf\small\red{Given:-}$

$\sf \rightarrow \: f(x) = {x}^{2} + x - 2$

$\sf\small\red{Find:-}$

$\sf \rightarrow \: find \: \alpha \: and \: \beta .$

$\sf\small\red{Solution:-}$

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

$\sf \rightarrow\: {x}^{2} + 2x - x - 2$

$\sf \rightarrow \: x(x + 2) - 1(x + 2)$

$\sf \rightarrow \: (x + 2)(x - 1) = 0$

$\sf \rightarrow \: x + 2 = 0$

$\sf \dashrightarrow \fbox \blue{ x = - 2}$

$\sf \rightarrow \: x - 1 = 0$

$\sf \dashrightarrow\fbox \blue{x = 1}$

Alpha = -2.

Bita = 1.

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