Question

Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain. Can you give me answers this time instead of putting something random just so you can get points.

Answer 1

Answer:

-2 and 2

just think about -2 and 2

Answer 2

Yes, it is possible and happens when the modulus of the numbers is the same i.e. they are just opposite in sign.

For some quadratic equation, $ax^{2} + bx + c = 0$ where a is not equal to zero, these results tell us that it can have at most two solutions.

The number of solutions refers to the number of times the graph of this equation will cut the x-axis. We can know whether the equation will have one, zero, or two real and distinct roots by finding the determinant.

$D = b^{2} - 4ac$

If,

D < 0, no real rots exist.

D = 0, one real root exists. The function touches the x-axis at a point.

D< 0, two distinct real roots exist.

In general, a polynomial's highest degree is the maximum number of real roots that can exist for that polynomial.