Multiple choice

Find the roots of equation: $\displaystyle 15{ x }^{ 2 }-2x-1=0$

  1. $\dfrac{-1}{3}, \dfrac {-1}{5}$
  2. $\dfrac{1}{3}, \dfrac {1}{5}$
  3. $\dfrac{1}{3}, \dfrac {-1}{5}$

  4. None
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C Correct answer
AI explanation

We can solve the quadratic equation 15x squared minus 2x minus 1 equals 0 using the factorization method. We split the middle term by finding two numbers that multiply to negative 15 and add to negative 2, which are negative 5 and 3. This gives 15x squared minus 5x plus 3x minus 1 equals 0, factoring to 5x times the quantity 3x minus 1 plus 1 times the quantity 3x minus 1 equals 0, so the factors are 5x plus 1 equals 0 and 3x minus 1 equals 0. Solving these yields the roots one third and negative one fifth.

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