Last updated at May 29, 2018 by Teachoo
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Example 13 Find the roots of the following quadratic equations, if they exist, using the quadratic formula: (i) 3x2 5x + 2 = 0 3x2 5x + 2 = 0 Comparing equation with ax2 + bx + c = 0 Here, a = 3, b = 5, c = 2 We know that, D = b2 4ac D = ( 5)2 4 (3) (2) D = 25 24 D = 1 So, the roots of the equation is given by x = ( )/2 Putting values x = ( ( 5) 1)/(2 3) x = (5 1)/6 Solving Hence, the roots of the equation are 1 and 2/3 . Example 13 Find the roots of the following quadratic equations, if they exist, using the quadratic formula: (ii) x2 + 4x + 5 = 0 x2 + 4x + 5 = 0 Comparing equation with ax2 + bx + c = 0 Here, a = 1, b = 4, c = 5 We know that D = b2 4ac D = (4)2 4 (1) (5) D = (4)2 20 D = 16 20 D = 4 Hence roots to equation are x = ( )/2 x = ( 4 ( 4))/(2 (1)) Since there is a negative number in the root, therefore D will not have any real value. So, there are no real roots for the given equation. Example 13 Find the roots of the following quadratic equations, if they exist, using the quadratic formula: (iii) 2x2 2 2 + 1 = 0 2x2 - 2 2 x + 1 = 0 Comparing equation with ax2 + bx + c = 0 Here, a = 2, b = 2 2 , c = 1 We know that D = b2 4ac = (" 2" 2)^2 4 (2) 1 = (4 2) (8) = 8 8 = 0 So, the roots of the equation is given by x = ( )/2 Putting values x = ( ( 2 2) 0)/(2 2) x = (2 2 0)/4 x = (2 2)/4 x = 2/2 Hence, the roots of the equation are 2/2 and 2/2.
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Example 5 Important
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Example 7 Deleted for CBSE Board 2022 Exams
Example 8 Important Deleted for CBSE Board 2022 Exams
Example 9 Deleted for CBSE Board 2022 Exams
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