Multiple choice

What are the roots of the quadratic equation 21x2 - 37x - 28 = 0?

  1. -7/3, 4/7

  2. 3/7, -7/4

  3. 7/3, -4/7

  4. -3/7, 7/4

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

21x^2 - 37x - 28 = 0. Using the quadratic formula: x = (37 +/- sqrt(37^2 - 4*21*(-28))) / 42 = (37 +/- sqrt(1369 + 2352)) / 42 = (37 +/- sqrt(3721)) / 42 = (37 +/- 61) / 42. Roots are 98/42 = 7/3 and -24/42 = -4/7.

AI explanation

Using the method of splitting the middle term, we rewrite the quadratic equation 21x^2 - 37x - 28 = 0 as 21x^2 - 49x + 12x - 28 = 0. Factoring by grouping gives 7x(3x - 7) + 4(3x - 7) = 0, which leads to (3x - 7)(7x + 4) = 0. Equating each factor to zero provides the roots x = 7/3 and x = -4/7.