Question

What is the sum of the squares of the roots of `x^2-5x+4=0`?

Answer 1

Sum of squares of roots is `17`.

Explanation:

In an equation of the type `ax^2+bx+c=0`, if roots are `alpha` and `beta`, then sum of roots `alpha+beta=-b/a` and product of the roots `alphabeta=c/a`.

As the given equation is `x^2-5x+4=0`, we have `alpha+beta=5` and `alphabeta=4`

As such sum of squares of roots i.e.

`alpha^2+beta^2`

= `alpha^2+beta^2+2alphabeta-2alphabeta`

= `(alpha+beta)^2-2alphabeta`

= `5^2-2xx4`

= `25-8`

= `17`