Question

Step 2 of 2 (Step 1, a = 1, b = 7, c = -2)Use the discriminant, b^2 - 4ac, to determine the number of solutions of the given quadratic equation. x^2 + 7x - 2 = 0Then solve the quadratic equation using the formula X = (Formula to use in the pic attached)

Answer 1

The equation:

$x^2+7x-2=0$

has the values a=1, b=7 and c=-2; hence the discriminant is:

$7^2-4(1)(-2)=49+8=57$

Since the disciminant is positive this means that the equation will have two different solutions.

The solutions can be found using the general formula:

$\begin{gathered} x=\frac{-7\pm\sqrt[]{7^2-4(1)(-2)}}{2(1)} \\ x=\frac{-7\pm\sqrt[]{57}}{2} \end{gathered}$

therefore the solutions are:

$\begin{gathered} x=-\frac{7}{2}+\frac{\sqrt[]{57}}{2} \\ \text{and} \\ x=-\frac{7}{2}-\frac{\sqrt[]{57}}{2} \end{gathered}$