Question

Decide how many solutions the equation has. $$x^{2}-2 x-15=0$$

Short answer

The equation \(x^{2}-2x-15=0\) has two solutions.

Step-by-step solution

Identify the coefficients

The quadratic equation is in the form \(ax^{2}+bx+c=0\). For our equation, \(x^{2}-2x-15=0\), the coefficients are \(a=1, b=-2,\) and \(c=-15\).

Compute the discriminant

Compute the discriminant D using the formula \(D=b^{2}-4ac\). In our case, D is \((-2)^{2} - 4*1*(-15)\) which simplifies to \(4+60=64\).

Find the number of solutions

Because our discriminant D is positive, this means our equation \(x^{2}-2x-15=0\) has two distinct solutions.