review 2

Given the quadratic equation 𝑥 2 − 4𝑥 + 4 = 0, calculate the discriminant and determine the nature of its roots.

• Discriminant = 0, Real and Equal Roots

• Discriminant > 0, Real and Unequal Roots

• Discriminant < 0, Imaginary Roots

• Discriminant = 4, Real and Equal Roots

How can the discriminant of a quadratic equation help in determining the nature of its roots?

• By providing the exact values of the roots.

• By indicating whether the roots are real or imaginary

• By simplifying the equation to its factored form.

• By graphing the equation to visualize the roots.

• The coefficient a affects the width and direction of the parabola, b determines the position of the vertex horizontally, and c controls the vertical position of the parabola.

• The coefficient a shifts the parabola up or down, b affects the slope of the parabola, and c determines the x-intercepts.

• The coefficient a determines the vertical stretch or compression and the direction of the parabola (upward or downward), b influences the location of the vertex along the x-axis, and c represents the y-intercept.

• The coefficient a affects the horizontal position of the parabola, b determines the vertical position of the parabola, and c adjusts the curvature of the parabola

• Multiply both sides by 𝑥 − 1 to eliminate the fraction, then simplify the resulting equation to identify it as a quadratic equation

• Divide both sides by 𝑥 − 1 to isolate x, and solve for x directly.

• Add 𝑥 − 1 to both sides of the equation to simplify the rational expression.

• Substitute 𝑥 − 1 into the equation to check if it is a solution

• The solutions are x = - 1 and x = - 2 , and both are valid for the original rational algebraic equation

• The solutions are x = - 1 and x = - 2 , but only one of them satisfies the original rational algebraic equation

• The solutions are x = 0 and x = - 2 , and neither satisfies the original rational algebraic equation.

• The solutions are x = 1 and x = 2 , but these values must be checked against any excluded values from the original rational expression.

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• The equation has exactly one real solution, which is zero.

• The equation has one solution, and it is a negative number.

• The equation has no real solutions; the solutions are complex numbers.

• The equation has two distinct real solutions, both of which are positive numbers

• 𝑥 = −1 𝑎𝑛𝑑 𝑥 = 5

• 𝑥 = 1 𝑎𝑛𝑑 𝑥 = −5

• 𝑥 = 1 𝑎𝑛𝑑 𝑥 = 5

• 1

• 0

• -1

• 2