Solving quadratic equations using square root

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the square root property?

Back

The square root property states that if x² = k, then x = ±√k.

Front

How do you solve x² = 121 using square roots?

Back

x = ±11.

Front

What are the solutions to the equation x² = -49?

Back

There are no real solutions because the square root of a negative number is not defined in the set of real numbers.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means that the graph of the equation does not intersect the x-axis, indicating that the solutions are complex or imaginary.

Front

How do you find the solutions of 4m² - 100 = 0?

Back

First, add 100 to both sides: 4m² = 100. Then divide by 4: m² = 25. Finally, take the square root: m = ±5.

Front

What are the solutions to the equation x² = 0?

Back

The solution is x = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.

Front

If the discriminant is positive, what can be said about the roots?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

If the discriminant is zero, what can be said about the roots?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).