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
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