Question

How do you factor and solve `2x^2+2x-2=0`?

Answer 1

this equation cannot be solved by factorization that means it takes a lot of effort and time and hence we have to use the quadratic formula.

Explanation:

given equation `x^2+x-1=0`
first we have to check the nature of the roots by using discriminant
`D=b^2-4ac` substituting the values of `b=1,a=1,c=-1` we get
`D=1+4=5>0` hence we have real and distinct roots
applying the quadratic formula`color(red)[(-b+-sqrt(b^2-4ac))/(2a)]rArr[(-1+-sqrt(1+4))/2]rArr(-1+-sqrt5)/2`
hence the roots are `(-1+-sqrt5)/2`