Question

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

2c2=16c−32



two rational solutions

two irrational solutions

one rational solution

two nonreal solutions

Answer 1

One rational solution.

Just took the test.

Answer 2

Answer: The answer is (C).

Step-by-step explanation: The given quadratic equation is

$2c^2=16c-32\\\\\Rightarrow c^2=8c-16\\\\\Rightarrow c^2-8c+16=0.$

We know that the type of the solution of a quadratic equation depends upon the discriminant.

Here, the discriminant is given by

$D=8^2-4\times 1\times 16=64-64=0.$

Since the discriminant is zero, so the two roots are real and equal.

Thus, we can say that the equation has one rational solution.

Hence, (C) is the correct option.