(a) Find the discriminant of the equation $5 x^{2}+5 x+7=0$.

Discriminant $=\square$ (Enter a numeric response)
(b) Based on the discriminant, determine whether the equation has two (distinct) solutions, one solution, or two complex solutions.

The equation has ?
(Select a response)

Answer

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Answer

Final Answer: The discriminant of the equation $5x^{2}+5x+7=0$ is $\boxed{-115}$.

Steps

Step 1 ：Let's find the discriminant of the equation $5x^{2}+5x+7=0$. The discriminant is given by the formula $D = b^{2} - 4ac$.

Step 2 ：Substitute $a = 5$, $b = 5$, and $c = 7$ into the formula.

Step 3 ：Calculate the discriminant $D = (5)^{2} - 4*5*7$.

Step 4 ：The discriminant $D = -115$.

Step 5 ：Since the discriminant is less than 0, the quadratic equation has two complex solutions.

Step 6 ：Final Answer: The discriminant of the equation $5x^{2}+5x+7=0$ is $\boxed{-115}$.