Math  /  Algebra

QuestionFind the real solutions, if any, using the quadratic formula. 7y2y+5=07 y^{2}-y+5=0
Select the correct choice below and fill in any answer boxes within your choice. A. The solution set is \square 3. (Simplify your answer. Use a comma to separate answers as needed.) B. There are no real solutions.

Studdy Solution

STEP 1

1. The equation is a quadratic equation of the form ay2+by+c=0 ay^2 + by + c = 0 .
2. The coefficients are a=7 a = 7 , b=1 b = -1 , and c=5 c = 5 .
3. We will use the quadratic formula to find the real solutions, if any.

STEP 2

1. Identify the coefficients.
2. Calculate the discriminant.
3. Determine the nature of the roots based on the discriminant.
4. Apply the quadratic formula to find the solutions, if they exist.

STEP 3

Identify the coefficients from the quadratic equation 7y2y+5=0 7y^2 - y + 5 = 0 :
- a=7 a = 7 - b=1 b = -1 - c=5 c = 5

STEP 4

Calculate the discriminant Δ\Delta using the formula Δ=b24ac\Delta = b^2 - 4ac:
Δ=(1)24×7×5 \Delta = (-1)^2 - 4 \times 7 \times 5 Δ=1140 \Delta = 1 - 140 Δ=139 \Delta = -139

STEP 5

Determine the nature of the roots based on the discriminant:
- Since Δ=139\Delta = -139 is less than zero, the quadratic equation has no real solutions.

STEP 6

Since the discriminant is negative, there are no real solutions to the quadratic equation. Therefore, the correct choice is:
B. There are no real solutions.
The solution to the problem is:
B. There are no real solutions.

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