Solving Quadratics by Factoring and 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 by factoring?

Back

To solve a quadratic equation by factoring means to express the equation in the form (px + q)(rx + s) = 0 and then set each factor equal to zero to find the values of x.

Front

What are the roots of the equation x² - 9x = 0?

Back

The roots of the equation x² - 9x = 0 are x = 0 and x = 9.

Front

How do you find the roots of a quadratic equation using the square root method?

Back

To find the roots using the square root method, isolate the x² term, take the square root of both sides, and solve for x.

Front

What is the value of i^4 in complex numbers?

Back

The value of i^4 is 1, since i is the imaginary unit and i^2 = -1.

Front

What are the solutions to the equation 2x² + 7x + 6 = 0?

Back

The solutions to the equation 2x² + 7x + 6 = 0 are x = -3/2 and x = -2.

Front

What is the difference between real and complex roots?

Back

Real roots are solutions that can be found on the number line, while complex roots include imaginary numbers and cannot be represented on the number line.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are two complex roots.

Front

How do you solve the equation x² - 49 = 0?

Back

To solve x² - 49 = 0, factor it as (x - 7)(x + 7) = 0, giving the solutions x = -7 and x = 7.

Front

What is the value of i^79 in complex numbers?

Back

The value of i^79 is -i, as the powers of i cycle every four: i, -1, -i, 1.