What happens if the discriminant is positive and is a perfect square give an example?

What happens if the discriminant is positive and is a perfect square give an example?

If the discriminant is a positive number, then there are 2 real solutions. This means that the graph of the parabola interepts the x-axis at 2 distinct points . If the discriminant is positive and also a perfect square like 64, then there are 2 real rational solutions.

What happens if the discriminant is positive?

A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

How many solutions if the discriminant is a perfect square?

If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational. If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational. Determine the nature of the solutions to each quadratic equation.

What if a quadratic equation is a perfect square?

Some quadratic expressions can be factored as perfect squares. For example, x²+6x+9=(x+3)². However, even if an expression isn’t a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn’t a perfect square, but if we add 4 we get (x+3)².

What are positive perfect squares?

A perfect square is an integer which is the square of another integer n , that is, n2 . (Since a negative times a negative is positive, a perfect square is always positive.

Why does a positive discriminant result in two solutions?

If the discriminant is positive, this means that you have a positive number under the square root in the quadratic formula. This means you will end up with 2 real solutions. You can always take the square root of a positive number. If there are 2 real solutions, this also means that the graph will have 2 x-intercepts.

What does a positive discriminant mean?

The discriminant is the term underneath the square root in the quadratic formula and tells us the number of solutions to a quadratic equation. If the discriminant is positive, we know that we have 2 solutions. If it is negative, there are no solutions and if the discriminant is equal to zero, we have one solution.

What is the condition of perfect square?

Basically, a perfect square is what you get when you multiply two equal integers by each other. 25 is a perfect square because you’re multiplying two equal integers (5 and 5) by each other.

How many perfect squares are there in 30?

The perfect squares table is given below in terms of squares of numbers from 1 to 50….Perfect Squares List.