My professor wants us to prove and state the quadratic formula theorem. He is so picky that he didn’t accept my previous answer for it. Any suggestions?

Thanks

February 5th, 2011 @5:28 pm

Hi,

Given the quadratic formula ax² + bx + c = 0, solve it by completing the square.

ax² + bx + c = 0

Move constant to the other side.

ax² + bx = -c

Divide every term by “a”.

x² + (b/a)x = -c/a

Complete the square on the left side. Multiply ½ times the x coefficient. Square the result and add that amount to both sides.

x² + (b/a)x = -c/a

½(b/a) = b/(2a) [b/(2a)]² = b²/(4a²)

x² + (b/a)x + b²/(4a²) = -c/a + b²/(4a²)

Factor the left side. Re-arrange the right side.

(x + b/(2a))² = b²/(4a²) – c/a

Re-write the right side with a common denominator of 4a².

(x + b/(2a))² = b²/(4a²) – 4ac/(4a²)

(x + b/(2a))² = (b² – 4ac)/(4a²)

Take the square root of both sides. Put a ± in front of the radical on the right side.

……. ……. …… _______

x + b/(2a) = ± ?(b² – 4ac)/(2a)

Get x alone.

……. ……. …. _______

x = -b/(2a) ± ?(b² – 4ac)/(2a)

… …. ._______

-b ± ?(b² – 4ac)

———————– = x

…….2a

This is the quadratic formula, so it can be derived from completing the square on a quadratic equation. I hope that helps!!

there is a theorem??