Multiple choice

Using factorization find roots of quadratic equation: $\displaystyle 10{ z }^{ 2 }-20=0$

  1. $\displaystyle \sqrt { 2 } ,-\sqrt { 2 } $
  2. $\displaystyle \sqrt { 2 } ,\sqrt { 2 } $
  3. $\displaystyle -\sqrt { 2 } ,-\sqrt { 2 } $

  4. None
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A Correct answer
Explanation

10z^2 - 20 = 0 implies z^2 = 2. Taking the square root of both sides gives z = sqrt(2) or z = -sqrt(2).

AI explanation

To find the roots using factorization, first isolate the squared term by dividing the equation 10z^2 - 20 = 0 by 10 to get z^2 - 2 = 0. This factors into (z - sqrt(2))(z + sqrt(2)) = 0 using the difference of squares identity. Setting each factor to zero gives the roots as sqrt(2) and -sqrt(2).

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