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(x+(13)/(2))(x-(13)/(2))=0 How many distinct real solutions does the given equation have? Choose 1 answer: (A) 0 (B) 1 (C) 2 (D) 3

(x+132)(x−132)=0 \left(x+\frac{13}{2}\right)\left(x-\frac{13}{2}\right)=0 \newlineHow many distinct real solutions does the given equation have?\newlineChoose 11 answer:\newline(A) 00\newline(B) 11\newline(C) 22\newline(D) 33

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Solve a quadratic equation using the zero product propertyright chevron icon

Full solution

Q. (x+132)(x−132)=0 \left(x+\frac{13}{2}\right)\left(x-\frac{13}{2}\right)=0 \newlineHow many distinct real solutions does the given equation have?\newlineChoose 11 answer:\newline(A) 00\newline(B) 11\newline(C) 22\newline(D) 33
  1. Question Prompt: question_prompt: ＂How many distinct real solutions does the given equation (x+132)(x−132)=0(x+\frac{13}{2})(x-\frac{13}{2})=0 have?＂
  2. Set First Factor: Step 11: Set the first factor, (x+132)(x+\frac{13}{2}), equal to 00.
  3. Solve for x: Step 22: Solve for x, so x=−132x = -\frac{13}{2}. That's one solution.
  4. Set Second Factor: Step 33: Now set the second factor, x−132x-\frac{13}{2}, equal to 00.
  5. Solve for x: Step 44: Solve for x again, so x=132x = \frac{13}{2}. That's another solution.
  6. Total Distinct Real Solutions: Step 55: We got two solutions, x=−132x = -\frac{13}{2} and x=132x = \frac{13}{2}, so there are 22 distinct real solutions.

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