Question

Answer please...takin the quiz noww
..How many and what type of solutions does the equation have?


2c2=16c−32


one rational solution

two irrational solutions

two rational solutions

two nonreal solutions

Answer 1

The given equation is $2c^2=16c-32$

We need to determine the type of solution and the number of solutions.

Solving the equation:

Let us solve the equation to determine the number of solution and the type of solution.

Subtracting both sides of the equation by 16c, we get;

$2c^2-16c=-32$

Adding both sides of the equation by 32, we have;

$2 c^{2}-16 c+32=0$

Let us solve the equation using the quadratic formula.

Thus, we have;

$c=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 2 \cdot 32}}{2 \cdot 2}$

Simplifying, we get;

$c=\frac{16 \pm \sqrt{{256}-256}}{4}$

$c=\frac{16 \pm \sqrt{0}}{4}$

$c=\frac{16}{4}$

$c=4$

Thus, the solution of the equation is 4.

Hence, the equation has one rational solution.

Therefore, Option A is the correct answer.