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How many and what type of solutions does the equation have?

2c² = 16c - 32
A) One real solution
B) Two real solutions
C) No real solutions
D) Infinite solutions

User Machour
by
8.3k points

1 Answer

2 votes

Final answer:

The quadratic equation 2c² = 16c - 32 has one real solution, determined by rearranging it to standard form and applying the quadratic formula, which results in a zero discriminant.

Step-by-step explanation:

The equation given, 2c² = 16c - 32, is a quadratic equation of the form at² + bt + c = 0. To determine the type and number of solutions, we can first rearrange the equation to standard form by moving all terms to one side: 2c² - 16c + 32 = 0. Next, we can apply the quadratic formula to find the solutions. The quadratic formula is given by (-b ± √(b² - 4ac)) / (2a), where a, b, and c are constants from the quadratic equation at² + bt + c = 0. In our case, a = 2, b = -16, and c = 32. We calculate the discriminant, Δ = b² - 4ac, to determine the nature of the solutions. Here, Δ = (-16)² - 4(2)(32) = 256 - 256 = 0. Since the discriminant is zero, the equation has one real solution.

User Reg Domaratzki
by
8.5k points
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