The quadratic equation 6x2−x−15=0
in factored form is
(1 point)
Responses
(3x−5)(2x−3)=0
(6x+5)(x−1)=0
(6x+5)(2x−3)=0
(3x−5)(2x+3)=0
which results in the solutions x=
5
−5
53
−65
and x=
−3
−32
3
1
To find the factored form of the quadratic equation 6x^2 - x - 15 = 0, we first need to determine the factors of the quadratic trinomial. Since the coefficient of x^2 is 6, we need to find factors of 6 that multiply to 6 and add up to -1 (the coefficient of x).
The factors of 6 are 1, 2, 3, and 6. We see that the combination 2 and 3 can be used to get -1 when added, so we rewrite the middle term as -3x + 2x.
Therefore, 6x^2 - 3x + 2x - 15 = 6x^2 - x - 15.
Now, factor by grouping:
(6x^2 - 3x) + (2x - 15)
3x(2x - 1) + 3(2x - 5)
3x(2x - 1) - 3(5 - 2x)
3x(2x - 1) - 3(2x - 5)
3x(2x - 1) - 3(2x - 1)
(3x - 5)(2x - 1)
Therefore, the factored form of the quadratic equation 6x^2 - x - 15 = 0 is (3x - 5)(2x - 1) = 0.
The solutions for x are:
3x - 5 = 0
3x = 5
x = 5/3
2x - 1 = 0
2x = 1
x = 1/2
Therefore, the solutions for x are x = 5/3 and x = 1/2.