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Solving Quadratic Equations Involving Fractions WORKSHEET
Suitable for Grades: Algebra II, IM 2
CCSS: HSA.REI.B.4
CCSS Description: Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation; recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Solving Quadratic Equations Involving Fractions WORKSHEET DESCRIPTION
This worksheet focuses on solving quadratic equations that involve fractions.
The initial problems require multiplying by x to clear the denominator, leading to a standard quadratic form. The progression continues with equations which introduce a numerical denominator, necessitating multiplication by both x and the constant to clear fractions.
Further on, problems involve a quadratic term in the denominator, requiring multiplication by x2 to eliminate fractions. The difficulty escalates when binomial expressions are present, demanding subsequent expansion and rearrangement to form the quadratic equation.
The final questions present more complex fractional expressions, leading to more intricate algebraic manipulations to achieve the standard quadratic form.
All but one of the twelve equations can be solved by factorising into double brackets after the manipulation. For the final question, we have used the quadratic formula in order to find the values of x.
The initial problems require multiplying by x to clear the denominator, leading to a standard quadratic form. The progression continues with equations which introduce a numerical denominator, necessitating multiplication by both x and the constant to clear fractions.
Further on, problems involve a quadratic term in the denominator, requiring multiplication by x2 to eliminate fractions. The difficulty escalates when binomial expressions are present, demanding subsequent expansion and rearrangement to form the quadratic equation.
The final questions present more complex fractional expressions, leading to more intricate algebraic manipulations to achieve the standard quadratic form.
All but one of the twelve equations can be solved by factorising into double brackets after the manipulation. For the final question, we have used the quadratic formula in order to find the values of x.
All worksheets are created by the team of experienced teachers at Cazoom Math.
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This solving quadratic equations involving fractions worksheet is designed for students in Algebra II and IM 2 and aligns with Common Core State Standards.