Solve using the quadratic formula: y = 3x² + 5x + 5. Use a calculator as needed, but leave in radical form, simplifying the square root as much as possible

Question

(-5 ± sqrt(35)) / 6

(5 ± sqrt(35)) / 6

(-5 ± i sqrt(35)) / 6

(-5 ± 5i sqrt(7)) / 6

(-5 ± sqrt(10)) / 6

Answer 1

 For the quadratic formula, you take the equation 0=ax²+bx+c, where a, b, and c are the numbers associated with x², x, and the last number, respectively. So here, a=3, b=5, and c=5. To solve for x, you plug those values into the quadratic formula, which is:

 

x= [-b + or - sqrt(b²-4ac)]/2a

 

Here, we are solving for x at y=0. So x= [-5 + or - sqrt(5² -4*3*5)]/(2*3), which simplifies:

x= [-5 + or - sqrt(25-60)]/6

 

x= [-5 + or - sqrt(-35)]/6

 

x= [-5 + or - i*sqrt(35)]/6, which is the third option down.

 

Recall that i is the square root of -1, so we start with sqrt(-35) = sqrt(-1*35) = sqrt(-1)*sqrt(35) = i*sqrt(35).

 

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