Question

For what value of the constant K does the equation K x² + 2x = 1 have two real solutions?

Answer 1

The quadratic equation is K x² + 2x = 1

Rewrite the given quadratic equation in standard form

 K x² + 2x - 1  =  0

For the equation to have two real roots the discriminent has to be positive.

Hence,

Discriminent (D) > 0

2^2 - 4(k)(-1)  >  0

4 + 4k  >  0

Subtract 4 from each side

4 + 4k - 4  >  0 - 4

4k  >  -4

Devide the total ineqality with 4

(4k) / 4  >  -4/4

k  >  -1

Answer :

For the values of k  >  -1 the quadratic equation has real roots.