Question

For the quadratic polynomial x2+x-4 find the value of alfa / beta + beta / alfa

Answer 1

Answer :

x² + x - 4

On comparing it with ax² + bx + c = 0.

a = 1

b = 1

c = - 4

We know that ;

α + β = - b/a

⇒ α + β = - 1

And,

αβ = c /a

αβ = - 4

Now,

( α + β )² = α² + β² + 2αβ

⇒ (-1)² = α² + β² + 2 * (-4)

⇒ α² + β² = 1 + 8

⇒ α² + β² = 9

$\frac{ \alpha }{\beta } + \frac{ \beta }{ \alpha } \\ \\ \frac{ \alpha {}^{2} + \beta {}^{2} }{ \alpha \beta } \\ \\ \frac{9}{ - 4} \\ \\ \fcolorbox{red}{yellow}{answer} \boxed{ \bf \frac{ - 4}{9} }$