Solving quadratics with square roots

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 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 of 16?

Back

+4, -4

Front

How do you determine if a quadratic equation has no solution?

Back

A quadratic equation has no solution if the expression under the square root (the discriminant) is negative.

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

Solve for x: 2x² + 12 = 4

Back

no solution

Front

Solve for x: 3x² - 4 = -1

Back

+3, -3

Front

What is the first step in solving x² - 4 = 76?

Back

Subtract 76 from both sides to isolate the x² term.

Front

Solve for x: x² - 4 = 76

Back

x = 4√5, -4√5

Front

What is the process to solve (3/4)x² + 3 = 29?

Back

First, subtract 3 from both sides, then multiply by 4/3 to isolate x².