How many real number solutions does the equation have? y=3x^2 - 5x - 5
a. one
b. two
c. no solutions
d. infinitely many solutions
and i will pick best and you: )

There is a maximum possible of 2 solutions since this is a polynomial (with a power of 2).

I'm not sure what the easiest way is to determine whether the solutions are real or complex, but I do know of a way that is simple enough to be performed by you . . .

Use the quadratic formula (this calculates the roots of a quadratic equation):

x₁ = [-b + √(b² - 4ac)]/(2a)
x₂ = [-b - √(b² - 4ac)]/(2a)

where:
y = ax² + bx + c
y = 3x² - 5x - 5

so . . .
a = +3
b = -5
c = -5

plug & chug and you get . . .

x₁ = [-3 + √(85)]/(6)
x₂ = [-3 - √(85)]/(6)

since the value under the square root sign is positive (i.e. √(85)), the roots x₁ & x₂ will be positive, and thus they'll have real solutions (note: if it was √(-85), the solution would involve a complex number, so it would not be a real solution)

 . . .  answer is . . . (b) two

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