Question

find the discriminant.
8 = -4q²
what type of solutions does the equation have?
one real solution
two real solutions
two complex (non - real) solutions

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a quadratic equation is \(ax^{2}+bx + c = 0\). Given \(8=-4q^{2}\), we can rewrite it as \(4q^{2}+8 = 0\), so \(a = 4\), \(b = 0\), \(c = 8\).

Step2: Recall the discriminant formula

The discriminant \(D\) of a quadratic equation \(ax^{2}+bx + c = 0\) is given by \(D=b^{2}-4ac\).

Step3: Calculate the discriminant

Substitute \(a = 4\), \(b = 0\), \(c = 8\) into the discriminant formula: \(D=(0)^{2}-4\times4\times8=0 - 128=- 128\).

Step4: Determine the type of solutions

• If \(D>0\), the equation has two real solutions.
• If \(D = 0\), the equation has one real solution.
• If \(D<0\), the equation has two complex (non - real) solutions.

Since \(D=-128<0\), the equation has two complex (non - real) solutions.

Answer:

The discriminant is \(-128\) and the equation has two complex (non - real) solutions.