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

1,000=20z2 1,000=20 z^{2} \newlineHow many distinct real solutions does the given equation have?\newlineChoose 11 answer:\newline(A) 00\newline(B) 11\newline(C) 22\newline(D) 44

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Full solution

Q. 1,000=20z2 1,000=20 z^{2} \newlineHow many distinct real solutions does the given equation have?\newlineChoose 11 answer:\newline(A) 00\newline(B) 11\newline(C) 22\newline(D) 44
  1. Simplify the equation: Simplify the equation to find the solutions for zz.\newlineWe start by dividing both sides of the equation by 2020 to isolate z2z^{2}.\newline1,000=20z21,000 = 20z^{2}\newlinez2=1,00020z^{2} = \frac{1,000}{20}\newlinez2=50z^{2} = 50
  2. Solve for z: Solve for z.\newlineTo find the values of z, we take the square root of both sides of the equation.\newlinez2=±50\sqrt{z^{2}} = \pm\sqrt{50}\newlinez = ±50\pm\sqrt{50}
  3. Simplify the square root: Simplify the square root.\newline50\sqrt{50} can be simplified to 25×2\sqrt{25\times2} which is 525\sqrt{2}.\newlineSo, z=±52z = \pm5\sqrt{2}
  4. Determine the number of solutions: Determine the number of distinct real solutions.\newlineSince we have a positive and a negative solution for zz, there are 22 distinct real solutions.

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