Question

10. If a, ß are the roots of ax2 + bx + c = 0, find the values of
(alpha/beta+beta/alpha)²
​

Answer 1

Answer:

Step-by-step explanation:

-b/a=sum of root=alpha+beta

c/a=product of root=alpha×beta

(alpha^2+beta^2/alpha ×beta)^2

{(Alpha+beta)^2-2(alpha×beta)/alpha×beta}^2

{(-b/a)^2-2c/a. Upon c/a}^2

{b^2/a^2-2c/a upon c/a}

{b^2-2ca upon c}^2

Answer 2

$\huge\mathbb\fcolorbox{pink}{lavenderblush}{♡Question}$

If a, ß are the roots of ax2 + bx + c = 0, find the values of

(alpha/beta+beta/alpha)²

$\huge\mathbb\fcolorbox{Green}{violet}{♡ᎪղՏωᎬя᭄}$

$\begin{gathered}\green{\tt{\therefore{{ \alpha }^{2} + { \beta }^{2} + \alpha \beta = \frac{ {b}^{2} - ac }{ {a}^{2} }}}}\\\end{gathered} ∴α 2 +β 2 +αβ= a 2 b 2 −ac$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\begin{gathered}\green{\underline{\bold{Given :}}} \\ \tt: \implies {ax}^{2} + bx + c = 0 \\ \\ \tt: \implies \alpha \: and \: \beta \: are \: roots \: of \: the \:eqn \\ \\ \red{\underline{\bold{To \: Find :}}} \\ \tt: \implies { \alpha }^{2} + { \beta }^{2} + \alpha \beta = ?\end{gathered}$

• According to given question :

${As \:we \: know \: that} \\ \tt: \implies Sum \: of \: roots = - \frac{ b}{a} \\ \\ \tt: \implies \alpha + \beta = - \frac{b}{a} - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Product \: of \: roots = \frac{c}{a} \\ \\ \tt: \implies \alpha \beta = \frac{c}{a} - - - - - (2) \\ \\ \bold{For \: finding \: values } \\ \tt: \implies { \alpha }^{2} + { \beta }^{2} + \alpha \beta \\ \\ \tt:$

Thanks!

TheEmeraldBoyy