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
General Properties of Quadratic Equation
Methods of Solving Quadratic Equations
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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