Answer:
x = 3, x = -1/6 are the zeros
Step-by-step explanation:
I find graphing the equation using a graphing calculator to be about the fastest way to find the zeros.
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For this equation, you can look for factors of 6·(-3) = -18 that have a sum of -17. Those are -18 and +1, so the factorization of the equation is ...
y = (1/6)(6x -18)(6x +1) = (x -3)(6x +1)
The roots are the values of x that make the factors be zero, so x=3 and x=-1/6.
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You can also use the quadratic formula to find the zeros. That tells you the solution to ...
ax² +bx +c = 0
is
x = (-b ±√(b²-4ac))/(2a)
Comparing your equation to the standard form, you can identify the coefficients as ...
a = 6, b = -17, c = -3
so the zeros are ...
x = (-(-17) ±√((-17)² -4(6)(-3)))/(2(6))
x = (17 ±√369)/12 = (17 ±19)/12 = {-2, 36}/12 = {-1/6, 3}
The zeros are x = -1/6 and x = 3.
