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$1,000=20z^{2}$ $\newline$ How many distinct real solutions does the given equation have? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $1$ $\newline$ (C) $2$ $\newline$ (D) $4$

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Full solution

Q.

1,000=20z^{2}

\newline

How many distinct real solutions does the given equation have?

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

1

\newline

(C)

2

\newline

(D)

4

Divide by $20$ : Given equation: $1,000 = 20z^{2}$ $\newline$ Divide both sides by $20$ to simplify the equation. $\newline$ $z^{2} = \frac{1,000}{20}$ $\newline$ $z^{2} = 50$
Take Square Root: Now we have a simplified equation: $z^{2} = 50$ $\newline$ To find the solutions for z, we take the square root of both sides. $\newline$ $z = \pm\sqrt{50}$
Two Real Solutions: Since we are taking the square root of a positive number ( $50$ ), we will have two real solutions: one positive and one negative. $\newline$ $z = \sqrt{50}$ or $z = -\sqrt{50}$
Distinct Solutions: The two solutions are distinct, as one is the negative of the other. Therefore, the equation has $2$ distinct real solutions.

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