Question

please help! will give medal
When solving an equation in the form ax^2=c by taking square roots, how many solutions will there be?

Answer 1

If we subtract c from both sides, we'd get: ax^2 - c =0.

This has an x^2 term, which means this represents some sort of parabola.

What do you know about parabolas? They have two roots, and cross the x-axis twice (at least the ones whose roots are not imaginary).

So there will be two solutions to ax^2 = c.

Answer 2

thank you! this makes a lot more sense now.

Answer 3

That is a geometrical approach. We can instead divide 'a' on both sides and get:

x^2 = c/a

And then we just take the square root:

x = sqrt[ c/a ].

However, where is the other answer? Well, the square root of a number is positive OR negative.

For example, take 25. You either multiply (5)*(5) and get 25, or you can multiply (-5)*(-5) to get 25!

So x = +sqrt[ c/a ]
x = -sqrt[ c/a ]

Answer 4

You're welcome!