How do you find the roots, real and imaginary, of y=−3x2+12x+14 using the quadratic formula?

1 Answer
Lucy
Aug 1, 2018

x=−0.94 and x=4.94

Explanation:

The general form of a quadratic equation is y=ax2+bx+c

The quadratic formula is x=−b±√b2−4ac2a where a,b,c are from the general form

Looking at y=−3x2+12x+14,
a=−3
b=12
c=14

x=−b±√b2−4ac2a

x=−12±√144+1682×−3

x=−12±√312−6

x=−12+√312−6 or x=−12−√312−6

Therefore, the roots are x=−0.94 and x=4.94
(both answers to 2.d.p)

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