390 Quadratic Equations with Complex Roots
which simplifies to
2 x^2 + 79 = 0
Here’s a challenge!
Investigate what happens in the general case if a is positive and c is negative in the quadratic equation
ax^2 +c= 0
Solution
We have a> 0 and c< 0. That means −c> 0. Let’s rewrite the above equation as
ax^2 − (−c)= 0
We can add −c to each side, getting
ax^2 =−c
Dividing through by a, we obtain
x^2 =−c/a
Because −c> 0 and a> 0, we know that −c/a> 0. We can take the positive-negative square root of both
sides to get
x=±(−c/a)1/2
Stated separately, the roots are
x= (−c/a)1/2 or x=−[(−c/a)1/2]
These are both real numbers, and are additive inverses.
Here’s another challenge!
Investigate what happens in the general case if a is negative and c is positive in the quadratic equation
ax^2 +c= 0
Solution
We have a< 0 and c> 0. That means −a> 0. We can subtract c from each side, getting
ax^2 =−c
Multiplying through by −1 gives us
(−a)x^2 =c