Question

Show all work to solve 3x^2-5x-2=0

Answer 1

1) Split the second term in 3x²-5x-2 into two terms.

•Multiply the coefficient of the first term by the constant term.
3 x -2 = -6

•Ask: Which two numbers add up to -5 and multiply to -6?
1 and -6

•Split -5x as the sum of and –6x.
3x2 + x – 6x – 2

2) Factor out common terms in the first two terms, then in the last two terms.

x(3x+1)-2(3x+1)


3) factor out the common term 3x+1.

(3x+1)(x-2)

Answer 2

The roots are {2, -1/3}

Explanation:

The coefficients of this quadratic function are a = 3, b = -5 and c = -2.

Let's use the quadratic formula to find the roots of the given 3x^2-5x-2=0.

The discriminant is b^2 - 4(a)(c), or (-5)^2 - 4(3)(-2), or 25 + 24 = 49.

Thus, the roots are:

-(-5)±√49 5 ± 7

x = ---------------- = ------------ = 2 and -1/3

2(3) 6