anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation…

anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation $\frac{1}{2}x^{2}+4x + 8 = 0$. which explanation could anderson provide?\nthe equation has no real number solutions because the discriminant is 0.\nthe equation has one real number solution because the discriminant is 0.\nthe equation has no real number solutions because the discriminant is less than 0.\nthe equation has two real number solutions because the discriminant is greater than 0.

anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation $\frac{1}{2}x^{2}+4x + 8 = 0$. which explanation could anderson provide?\nthe equation has no real number solutions because the discriminant is 0.\nthe equation has one real number solution because the discriminant is 0.\nthe equation has no real number solutions because the discriminant is less than 0.\nthe equation has two real number solutions because the discriminant is greater than 0.

Answer

Explanation:

Step1: Identify coefficients

For the quadratic equation $\frac{1}{2}x^{2}+4x + 8=0$, we have $a=\frac{1}{2}$, $b = 4$, $c = 8$.

Step2: Calculate the discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(4)^{2}-4\times\frac{1}{2}\times8$. First, calculate $(4)^{2}=16$, and $4\times\frac{1}{2}\times8 = 16$. Then $\Delta=16 - 16=0$.

Step3: Determine the number of real - solutions

If $\Delta = 0$, the quadratic equation has one real number solution.

Answer:

The equation has one real number solution because the discriminant is 0.