How do you find the roots, real and imaginary, of y=−x2+32x−16 using the quadratic formula?

2 Answers
M7chael
Oct 7, 2017

x=16+√240=31.49 OR x=16−√240=.51

There are no imaginary roots.

Explanation:

Quadratic formula:

For y=ax2+bx+c

x=−b±√b2−4ac2a

In your problem, a=−1,b=32,c=−16

So, x=−32±√322−4(−1)(−16)2(−1)

Simplifying:

x=−32±√1024−64−2

x=−32±√960−2

x=−32−2±√4⋅240−2

x=16±2√240−2

So x=16+√240=31.49 OR x=16−√240=.51

There are no imaginary roots.

Shwetank Mauria
Oct 7, 2017

Roots are 16−4√15 and 16+4√15

Explanation:

According to quadratic formula, the roots of y=ax2+bx+c are

−b±√b2−4ac2a

Hence roots of y=−x2+32x−16 are

−32±√322−4×(−1)(−16)2×(−1)

= −32±√1024−64−2

= 16±√9602

= 16±8√152

= 16±4√15

Related questions
See all questions in Quadratic Formula
Impact of this question
1935 views around the world
You can reuse this answer
Creative Commons License