Solving quadratics using square roots

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does it mean to solve a quadratic equation using square roots?

Back

Solving a quadratic equation using square roots involves isolating the x² term and then taking the square root of both sides to find the values of x.

Front

What is the square root property?

Back

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

Front

How do you isolate x² in the equation x² + 4 = 68?

Back

Subtract 4 from both sides to get x² = 64.

Front

What are the solutions to the equation x² = 64?

Back

The solutions are x = ±8.

Front

How do you solve the equation 7x² + 1 = 8 using square roots?

Back

First, subtract 1 from both sides to get 7x² = 7, then divide by 7 to get x² = 1, and finally take the square root to find x = ±1.

Front

What is the solution set for the equation x² = 25?

Back

The solution set is {5, -5}.

Front

How do you solve the equation 5b² - 4 = 41?

Back

Add 4 to both sides to get 5b² = 45, then divide by 5 to get b² = 9, and take the square root to find b = ±3.

Front

What are the solutions to the equation k² - 6 = 43?

Back

The solutions are k = ±7.

Front

What is the importance of the discriminant in solving quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.