Multiple choice

Solve the following quadratic equation by factorization, $3\sqrt{5}x^2 \, + \, 25x \, - \, 10\sqrt{5} \, = \, 0$ the roots are

  1. $\dfrac{\sqrt5}{2}$ $ , -2\sqrt{5}$
  2. $\dfrac{\sqrt5}{3}$ $ , -2\sqrt{5}$
  3. $\dfrac{\sqrt5}{5}$ $ , -2\sqrt{5}$
  4. $\dfrac{\sqrt5}{2}$ $ , -2\sqrt{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

3*sqrt(5)x^2 + 25x - 10*sqrt(5) = 0. Multiply by sqrt(5): 15x^2 + 25*sqrt(5)x - 50 = 0. Divide by 5: 3x^2 + 5*sqrt(5)x - 10 = 0. Using quadratic formula: x = (-5*sqrt(5) +/- sqrt(125 - 4*3*(-10))) / 6 = (-5*sqrt(5) +/- sqrt(245)) / 6 = (-5*sqrt(5) +/- 7*sqrt(5)) / 6. Roots are 2*sqrt(5)/6 = sqrt(5)/3 and -12*sqrt(5)/6 = -2*sqrt(5).

AI explanation

To factor 3*sqrt(5)x^2 + 25x - 10*sqrt(5) = 0 by splitting the middle term, we rewrite it as 3*sqrt(5)x^2 + 30x - 5x - 10*sqrt(5) = 0. Factoring by grouping gives 3x(sqrt(5)x + 10) - sqrt(5)(sqrt(5)x + 10) = 0, which simplifies to (3x - sqrt(5))(sqrt(5)x + 10) = 0. Setting the factors to zero gives x = sqrt(5)/3 and x = -10/sqrt(5), which simplifies to x = -2*sqrt(5).

Keep practicing — related questions