Question

If alpha and beta are zeroes of x^2+5x+5 then find the value of alpha - beta

Answer 1

Step-by-step explanation:

$let \: \alpha \: and \: \beta \: are \: the \ \\ : zeroes \: of \: the \: polynomial$

$given - quadratic \: equation \: is \: \\ = x {}^{2} + 5x + 5$

$we \: know \: that \: \\ \alpha + \beta = - \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

$\alpha + \beta = \frac{ - 5}{1}$

$so \\ \alpha + \beta = - 5 \\ \beta = - 5 - \alpha ........eq.1$

$now \: \\ \alpha \beta = \frac{constant}{coefficient \: of \: {x}^{2} }$

$\alpha \beta = \frac{5}{1} \\ \alpha \beta = 5$

$putting \: the \: value \: of \: \beta . \\ \alpha \beta = 5 \\ \alpha \times { - 5 - \alpha } = 5 \\ - 5 \alpha - { \alpha }^{2} = 5 \\ { \alpha }^{2} + 5 \alpha - 5 = 0$