Does the equation x^2=-64 have real solutions?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation ax^2+bx+c = 0 has a real solution if b^2-4ac>=0

We have to determine if x^2=-64 has real solutions.

x^2=-64

=> x^2 + 64 = 0

b^2 - 4ac = -4*64 = -256 which is less than 0.

The equation x^2=-64 does not have a real solution.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Of course, not!

There is no real number that raised to square to give a negative value.

But the equation has complex solutions.

x1 = +sqrt(-64) =>x1 = 8i

x2 = -sqrt(-64) => x2 = -8i

Keep in mind that complex solutions always come in pairs!

Therefore, the given equation has no real solutions.

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