Worksheet on Quadratic Formula

Practice the questions given in the worksheet on quadratic formula. We know the solutions of the general form of the quadratic equation ax\(^{2}\) + bx + c = 0 are x = \(\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\).


1. Answer the following:

(i) Is it possible to apply quadratic formula in the equation 2t\(^{2}\) +(4t - 1)(4t + 1) = 2t(9t - 1)

(ii) What type of equations can be solved using quadratic formula?

(iii) Applying quadratic formula, solve the equation (z - 2)(z + 4) = - 9

(iv) Applying quadratic formula in the equation 5y\(^{2}\) + 2y - 7 = 0, we get y = \(\frac{k ± 12}{10}\), What is the value of K?

(v) Applying quadratic formula in a quadratic equation, we get

                              m = \(\frac{9 \pm \sqrt{(-9)^{2} - 4 ∙ 14 ∙ 1}}{2 ∙ 14}\). Write the equation.

 

2. With the help of quadratic formula, solve each of the following equations:

(i) x\(^{2}\) - 6x = 27

(ii) \(\frac{4}{x}\) - 3 = \(\frac{5}{2x + 3}\)

(iii) (4x - 3)\(^{2}\) - 2(x + 3) = 0

(iv) x\(^{2}\) - 10x + 21 = 0

(v) (2x + 7)(3x - 8) + 52 = 0

(vi) \(\frac{2x + 3}{x + 3}\) = \(\frac{x + 4}{x + 2}\)

(vii) x\(^{2}\) + 6x - 10 = 0

(viii) (3x + 4)\(^{2}\) - 3(x + 2) = 0

(ix) √6x\(^{2}\) - 4x - 2 √6 = 0

(x) (4x - 2)\(^{2}\) + 6x - 25 = 0

(xi) \(\frac{x - 1}{x - 2}\) + \(\frac{x - 3}{x - 4}\) = 3\(\frac{1}{3}\)

(xii) \(\frac{2x}{x - 4}\) + \(\frac{2x - 5}{x - 3}\) = 8\(\frac{1}{3}\)


Answers for the worksheet on quadratic formula are given below.


Answers:


1. (i) No

(ii) Quadratic equation in one variable

(iii) -1, -1

(iv) K = -2

(v) 14m\(^{2}\) - 9m + 1 = 0

 

2. (i) -3 or 9

(ii) -2 or 1

(iii) x = \(\frac{3}{2}\) or \(\frac{1}{8}\)

(iv) 3 or 7

(v) x = -\(\frac{4}{3}\) or \(\frac{1}{2}\)

(vi) ±√6

(vii) -3 ± √19

(viii) x = -\(\frac{5}{3}\) or -\(\frac{2}{3}\)

(ix) √6 or -\(\frac{√6 }{3}\)

(x) x = -\(\frac{7}{8}\) or \(\frac{3}{2}\)

(xi) 2\(\frac{1}{2}\) or 5

(xii) 3\(\frac{1}{13}\) or 6

Quadratic Equation

Introduction to Quadratic Equation

Formation of Quadratic Equation in One Variable

Solving Quadratic Equations

General Properties of Quadratic Equation

Methods of Solving Quadratic Equations

Roots of a Quadratic Equation

Examine the Roots of a Quadratic Equation

Problems on Quadratic Equations

Quadratic Equations by Factoring

Word Problems Using Quadratic Formula

Examples on Quadratic Equations 

Word Problems on Quadratic Equations by Factoring

Worksheet on Formation of Quadratic Equation in One Variable

Worksheet on Quadratic Formula

Worksheet on Nature of the Roots of a Quadratic Equation

Worksheet on Word Problems on Quadratic Equations by Factoring







9th Grade Math

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