Question

What is true about the solutions of x2 − 2x − 15 = 0?

Answer 1

No real solutions
Two identical rational solutions
Two different rational solutions
Two irrational solutions

Answer 2

Using the quadratic formula. The discriminant \[b^2-4ac = (-2)^2-4(1)(-15)=64\] is greater than zero so there can't be no real solutions. So it must be either of the three remaining choices.

Answer 3

Also the discriminant is not equal to zero so there can't be two identical rational solutions.

Answer 4

You see a quadratic where \[b^2-4ac<0\] has no real solutions. A quadratic with \[b^2-4ac>0\] has 2 real or 2 irrational solutions. And a quadratic with \[b^2-4ac=0\] has two identical solutions.

Answer 5

We are down to the two choices two different irrational solutions and two different rational solutions. To have rational solutions the discriminant must be a perfect square. And in my first post I calculated it to be 64 which is a perfect square. So the quadratic equation has two rational solutions.

Answer 6

The answer is two rational solutions.

Answer 7

I mean two different rational solutions