Factor 6x² + 2x - 21?

Solution:

The given equation i.e. 6x2 + 2x - 21 is a quadratic equation of the form ax² + bx + c

a = 6, b = 2, c = 21

b² - 4ac = (2)² - 4 × 6 × (-21) = 4 + 504 = 508

The roots of the equation are as follows:

The roots of the quadratic equation ax² +bx + c are:

(1) (-b/2a) + (√b² - 4ac)/2a = [-2/(2 × 6)] + (√2² - 4× 6 × 21)/(2 × 6) = (-1/6) + √508/12 = (-1/6) + √254/6

(2) (-b/2a) - (√b² - 4ac)/2a = [-2/(2 × 6)] - (√2² - 4× 6 × 21)/(2 × 6) = (-1/6) - √508/12 = (-1/6) - √254/6

The two factors of the equation are:

(x - (-1 + √127)/6) and (x - (1 - √127)/6)

Factor 6x² + 2x - 21

Summary:

Factoring 6x² + 2x - 21 we get the factors (x - (-1 + √254)/6) and (x - (1 - √254)/6)