Question

Which equation has two real solutions?

A. x^2 = –100
B. 5x^2 = 1
C. 6x^2 + 17 = 11
D. 7(x^2 + 6) = 42

Answer 1

A. x^2 = –100

B. 5x^2 = 1

Explanation:

A.x^2=-100

have two solutions

x = 10

x = -10

B.5x^2=1

have two solutions

x = ±√ 0.200 = ± 0.44721

Answer 2

Hey there!

`\boxed{B.\space 5x^2=1}`

Let's solve each equation one by one to figure out which one is correct.

A.

x^2 = -100

Square root both sides.

x = √-100

A square root of a negative number is not a real number, so this option is incorrect.

B.

5x^2 = 1

Divide each side by 5.

x^2 = 1/5

Find the square root of each side.

x = ±0.447

The two solutions are positive 0.447 and -0.447 because those both equal 1/5 when squared. So this is the equation that has two real solutions. But let's keep solving to show why the other answers are wrong.

C.

6x^2 + 17 = 11

Subtract 17 from each side.

6x^2 = -6

Divide each side by 6

x^2 = -1

Square root each side.

x = √-1

A square root of a negative number is not a real number, so this option is incorrect.

D.

7(x^2 + 6) = 42

Divide each side by 7.

x^2 + 6 = 6

Subtract 6 from each side.

x^2 = 0

Square root of each side.

x = √0 = 0

The square root of 0 is just 0, there is only one solution.

So, the answer is B.

Hope this helps!