Question

How do you solve `2x^2 - 10x + 7 = 0` using the quadratic formula?

Answer 1

`x=(5+sqrt11)/2` or `x=(5-sqrt11)/2`

Explanation:

Quadratic formula gives the solution of a quadratic equation. For a quaddratic equation `ax^2+bx+c=0`, the roots given by quadratic formula are `(-b+-sqrt(b^2-4ac))/(2a)`.

Hence for `2x^2-10x+7=0`, we have `a=2`, `b=-10` and `c=7` and hence solution is

`(-(-10)+-sqrt((-10)^2-4*2*7))/(2*2)`

= `(10+-sqrt(100-56))/4`

= `(10+-sqrt44)/4`

= `(10+-2sqrt11)/4`

i.e. either `x=(5+sqrt11)/2` or `x=(5-sqrt11)/2`