Quadratic Equations and Simplification

The video tutorial explains how to solve a quadratic equation using the quadratic formula. It begins by setting the equation in the correct form, identifying coefficients, and substituting them into the formula. The process involves simplifying the square root and finding the solutions. Two methods for simplification are demonstrated, ensuring a comprehensive understanding of solving quadratic equations.

What is the first step in solving a quadratic equation using the quadratic formula?

• Divide the equation by the highest coefficient

• Multiply all terms by a constant

• Rearrange the equation to equal zero

• Identify the roots of the equation

What form should a quadratic equation be in to apply the quadratic formula?

• AX^2 + BX + C = 0

• AX + B = C

• AX^2 = BX + C

• AX^2 + C = BX

After rearranging the equation, what are the values of A, B, and C in the equation 9X^2 + 12X - 3 = 0?

• A = -3, B = 12, C = 9

• A = 12, B = 9, C = 3

• A = 3, B = 9, C = 12

• A = 9, B = 12, C = -3

What is the result of substituting the coefficients into the quadratic formula for the equation 9X^2 + 12X - 3 = 0?

• X = -12 ± √(144 + 108) / 18

• X = -12 ± √(144 - 108) / 18

• X = -12 ± √(144 + 108) / 9

• X = -12 ± √(144 - 108) / 9

What is the prime factorization of 252?

• 2 x 2 x 3 x 3 x 7

• 2 x 3 x 3 x 7

• 2 x 2 x 3 x 7

• 2 x 3 x 3 x 3 x 7

How can the expression X = -12 ± 6√7 / 18 be simplified?

• X = -2/3 ± √7/3

• X = -2 ± √7/3

• X = -12/18 ± √7/3

• X = -2/3 ± 6√7/3

What is one method to simplify the expression X = -12 ± 6√7 / 18?

• Break it into two separate fractions

• Multiply the numerator by 2

• Add 6 to both sides

• Divide the denominator by 2

What is the common factor used to simplify the fractions in the expression X = -12 ± 6√7 / 18?

• 9

• 2

• 3

• 6

What is the final simplified form of the solution for the quadratic equation?

• X = -2 ± √7/3

• X = -2/3 ± 6√7/3

• X = -12/18 ± √7/3

• X = -2/3 ± √7/3

Why is it important not to simplify across addition or subtraction in the expression X = -12 ± 6√7 / 18?

• It changes the equation's form

• It is unnecessary for solving

• It makes the equation more complex

• It would lead to incorrect simplification