Question

Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0 0 cannot be determined 1 2

Answer 1

No real solutions, or 0

Step-by-step explanation:

We can determine how many real solutions a quadratic function has, we can use the quadratic formula.

The quadratic formula for expressions written in ax² + bx + c form is:


`x = \frac{-b +/- \sqrt{b^(2)-4ac}}{2a}`

In the equation x² + 5x + 7, a = 1, b = 5 and c = 7

When we plug them in, we get:


`x = (-5 +/-√(5^2 - 4(1)(7)))/(2(1))\\ \\= (-5+/-√(25 - 28))/(2)\\ \\=(-5+/-√(-3))/(2)}`

We cannot find the square root of a negative number without diving into the realm of imaginary numbers in which √-3 becomes i√3. Therefore, the equation has no real solutions. This is because the equation x² + 5x + 7 is an upward-facing parabola translated up 7 units and, as such, does not cross the x-axis. If the equation yields a graph that does not cross the x-axis, then there will be zero answers for what variable x equals.