Question

complex numbers online practice
complete this assessment to review what youve learned. it will not count toward your grade.
show that the fundamental theorem of algebra is true for the quadratic polynomial $-2x^2 + 4x - 9 = 0$ by using the quadratic formula. which of the following statements accurately describes the solution set? (1 point)

there are two rational solutions.

there are two non-real solutions.

there are two identical solutions.

there are two irrational solutions.

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula for a quadratic equation \(ax^{2}+bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For the equation \(-2x^{2}+4x - 9 = 0\), we have \(a=-2\), \(b = 4\), \(c=-9\).

Step2: Calculate the Discriminant

The discriminant is \(D=b^{2}-4ac\). Substitute the values: \(D=(4)^{2}-4\times(-2)\times(-9)=16 - 72=- 56\).

Step3: Analyze the Discriminant

Since the discriminant \(D=-56<0\), the square root of a negative number is non - real. So, the solutions \(x=\frac{-4\pm\sqrt{-56}}{2\times(-2)}\) will be non - real. The quadratic equation is of degree 2, so there are two non - real solutions.

Answer:

There are two non - real solutions.