(t+15)^(2)+5=0 How many distinct real solutions does the given equation have? Choose 1 answer: (A) 0 (B) 1 (C) 2 (D) 4

Given equation: We are given the equation (t+15)^(2)+5=0 and we need to find the number of distinct real solutions. First, we will try to isolate the squared term by subtracting 5 from both sides of the equation. (t+15)^(2) + 5 - 5 = 0 - 5 (t+15)^(2) = -5Isolating the squared term: Now, we observe that the left side of the equation is a square of a real number, which can never be negative since squaring any real number always gives a non-negative result. Therefore, (t+15)^(2) cannot equal -5 for any real number t. This means there are no real solutions to the equation.

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(t+15)^(2)+5=0
How many distinct real solutions does the given equation have?
Choose 1 answer:
(A) 0
(B) 1
(C) 2
(D) 4

$(t+15)^{2}+5=0$ $\newline$ 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

(t+15)^{2}+5=0

\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

Given equation: We are given the equation $(t+15)^{2}+5=0$ and we need to find the number of distinct real solutions. $\newline$ First, we will try to isolate the squared term by subtracting $5$ from both sides of the equation. $\newline$ $(t+15)^{2} + 5 - 5 = 0 - 5$ $\newline$ $(t+15)^{2} = -5$
Isolating the squared term: Now, we observe that the left side of the equation is a square of a real number, which can never be negative since squaring any real number always gives a non-negative result. $\newline$ Therefore, $(t+15)^{2}$ cannot equal $-5$ for any real number $t$ . $\newline$ This means there are no real solutions to the equation.