Question

The roots of quadric equations 6x² - 5x - 21 = 0 are
1. \(-\frac{7}{3}, -\frac{3}{2}\)
2. \(\frac{7}{3}, \frac{3}{2}\)
3. \(\frac{7}{3}, -\frac{3}{2}\)
4. \(-\frac{7}{3}, \frac{3}{2}\)

Answer 1

Correct Answer - Option 3 : \(\frac{7}{3}, -\frac{3}{2}\)

Given

6x2 - 5x - 21 = 0 

Concept used

Quadratic equation

Calculation

⇒ 6x² - 14x + 9x - 21 = 0

⇒ 2x(3x - 7) + 3(3x - 7)

⇒ (2x + 3) (3x - 7)

Where 2x + 3 = 0 and 3x - 7 = 0

⇒ 2x + 3 = 0

⇒ 2x = -3

⇒ x = -3/2

⇒ 3x - 7 = 0

⇒ 3x = 7

⇒ x = 7/3

Two root equations are x = -3/2 and 7/3