Multiple choice

Find the sum of the roots of equation $(2x - 1)\left (\dfrac{3x}{2}+ 1\right ) = 0$

  1. $\dfrac{1}{6}$
  2. $\dfrac{-1}{6}$
  3. $\dfrac{-1}{3}$
  4. $\dfrac{-1}{2}$
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B Correct answer
Explanation

The equation is (2x - 1)(3x/2 + 1) = 0. Setting each factor to zero gives 2x - 1 = 0 (x = 1/2) and 3x/2 + 1 = 0 (x = -2/3). The sum of the roots is 1/2 - 2/3 = 3/6 - 4/6 = -1/6.

AI explanation

Setting each linear factor of (2x - 1)(3x/2 + 1) = 0 to zero gives the roots x = 1/2 and x = -2/3. The sum of these roots is 1/2 + (-2/3). Finding a common denominator of 6 gives the sum as 3/6 - 4/6 = -1/6.

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