Question

What is the roots of the quadratic equation? 6x^2+5x-4=0

Answer 1

x = $\frac{1}{2}$ or x = - $\frac{4}{3}$

consider the factors of the product 6 × - 4 = - 24 which sum to the coefficient of the x- term ( + 5)

the factors are + 8 and - 3 ( split the middle term using these factors

6x² - 3x + 8x - 4 = 0 ( factor by grouping )

3x(2x - 1) + 4(2x - 1 ) ( take out common factor of (2x - 1) )

= (2x - 1)(3x + 4) = 0

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ x = $\frac{1}{2}$

3x + 4 = 0 ⇒ x = - $\frac{4}{3}$

Answer 2

6x² + 5x - 4 = 0        

Multiply the first and last term (6x² * -4) to get -24x².  Now find two factors of -24x² whose sum is the middle term (5x).  -3x + 8x   Replace 5x with -3x + 8x, then factor and solve.

6x² - 3x    + 8x - 4 = 0

3x(2x - 1)  +4(2x - 1) = 0

(3x + 4) (2x - 1) = 0

3x + 4 = 0   or   2x - 1 = 0

x =  $-\frac{4}{3}$          or    x = $\frac{1}{2}$

Note: you can also use the quadratic formula to find the foots.