Question

Select the two values of x that are roots of this equation.

2x²11x+15=0
A. x = 6
B. x = 5
C. X-2/2
X=
D. x = 3

Answer 1

The roots are: x = -5/2, x = 3

Explanation:

Alternatively, you could factor out the left-hand side of the equation. There is a specific way that streamlines this process called the AC method: in a quadratic equation ax^2 + bx + c, the polynomial can be factored if there are two factors of a * c whose sum is b.

a * c here is 2 * 15 = 30, and we need to find out what factor pair of 30 sums to 11.

(30, 1) (15, 2) (10, 3) (6, 5)

6 + 5 = 11, so now, we put it back in like this:

2x^2 + 6x + 5x + 15

Now we can factor it:

2x(x + 3) + 5(x + 3)

(2x + 5)(x + 3)

Now that it's factored, we set this equal to 0.

(2x + 5)(x + 3) = 0

Either 2x + 5 or x + 3 = 0, and we can solve for this:

2x + 5 = 0

2x = -5

x = -5/2

x + 3 = 0

x = -3

I hope this helps.

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