What is the first step in using the Square Roots Method to solve an equation like $$2x^2 - 3 = -3$$ ?

The first step is to isolate the term with the variable squared, which in this case would be $$2x^2 = 0$$ .

What is the solution to the equation $$-3x^2 + 297 = 0$$ using the Square Roots Method?

$$x = -3\\sqrt{11}, 3\\sqrt{11}$$ .

Solve the equation using the Square Roots Method: $$10 - 2x^2 = -98$$

$$x = -3\\sqrt{6}, 3\\sqrt{6}$$ .

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

It means that the discriminant (b^2 - 4ac) is less than zero, indicating that the roots are complex.

What is the discriminant in a quadratic equation and how is it used?

The discriminant is given by $$b^2 - 4ac$$ and determines the nature of the roots of the quadratic equation.

Explain how to simplify a square root, for example $$\text{simplifying } \\sqrt{50}$$ .

To simplify $$\text{the square root } \\sqrt{50}$$ , factor it into $$\text{its prime factors: } 25 \times 2$$ , so $$\text{it simplifies to } 5\\sqrt{2}$$ .

What is the significance of isolating the variable squared in the Square Roots Method?

Isolating the variable squared allows you to take the square root of both sides, which is essential for solving the equation.

Provide an example of a quadratic equation that can be solved using the Square Roots Method.

An example is $$x^2 = 16$$ , which can be solved to find $$x = 4, -4$$ .

What is the relationship between the coefficients of a quadratic equation and its roots?

The coefficients of a quadratic equation relate to its roots through Vieta's formulas, which state that the sum and product of the roots can be expressed in terms of the coefficients.

Simplifying & Solving Quadratics by Square Roots Flashcards

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1.

FLASHCARD QUESTION

Front

Define the Square Roots Method in solving quadratic equations.

Back

The Square Roots Method involves isolating the variable squared on one side of the equation and then taking the square root of both sides to solve for the variable.

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CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is the general form of a quadratic equation?

Back

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