Review: Solve Quadratics with Square Roots

Front

What is the general form of a quadratic equation?

Back

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

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve a quadratic equation by taking square roots, isolate the x² term, then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What is the square root of a negative number represented by?

Back

The square root of a negative number is represented by an imaginary unit 'i', where i = √-1.

Front

What does i² equal?

Back

i² = -1.

Front

If 5m² + 1 = 6, what is the value of m?

Back

m = 1 or m = -1.

Front

How do you simplify √(a²)?

Back

√(a²) = |a|, which means the absolute value of a.

Front

What is the solution to the equation 7x² = 84?

Back

x = 2√3 or x = -2√3.

Front

What is the first step in solving 5b² - 4 = 41?

Back

Add 4 to both sides to isolate the b² term: 5b² = 45.

Front

What is the square root of 0?

Back

The square root of 0 is 0.

Front

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

Back

It means the discriminant (b² - 4ac) is less than 0, indicating that the roots are complex.