Question

given a quadratic equation in standard form f(x) = ax^2 + bx + c. explain how to determine if there is one real solution, two real solutions, or no real solutions (use the discriminant b^2 - 4ac)

Answer 1

As per given by the question,

There are given that a general form od quadratic equation.

The equation is,

`f(x)=ax^2+bx+c`

Now,

For determine the one real solution, two real solution, and no real solution;

There are apply the condition for all these three.

So,

First for one real solution.

If

`b^2-4ac=0,\text{ then}`

The given quadratic equation has one real solution.

If,

`b^2-4ac>0,\text{ then;}`

The given quadratic equation has two real solution.

And,

If,

`b^2-4ac<0,\text{ then;}`

The given quadratic equation has no real solution.