Find the values of k for which each of the following quadratic equation equal roots : (i) 9x 2 + kx + 1 = 0 (ii) x 2 - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

(i) The given equation is 9x 2 + kx + 1 = 0. Comparing with ax 2 + bx + c = we obtain, a = 9 , b = k , c = 1 For equal roots, discriminant = 0 When k = 6 the equation becomes 9x 2 + 6x + 1 = 0 so the roots are : The roots of the equation are given by When k = -6 the equation becomes 9x 2 - 6x + 1 = 0 so the roots are : The roots of the equation are given by Hence, the values of k are 6, -6 ; when k = 6, roots are and when k = -6, roots are . (ii) The given equation is x 2 - 2kx + 7k - 12 = 0. Comparing with ax 2 + bx + c = we obtain, a = 1 , b = -2k , c = 7k - 12 For equal roots, discriminant = 0 When k = 3 the equation becomes x 2 - 6x + 9 = 0 so the roots are : The roots of the equation are given by When k = 4 the equation becomes x 2 - 8x + 16 = 0 so the roots are : The roots of the equation are given by Hence the values of k are 3, 4 ; when k = 3, roots are 3, 3 and when k = 4, roots are 4, 4.

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Mathematics

Find the values of k for which each of the following quadratic equation equal roots :
(i) 9x² + kx + 1 = 0
(ii) x² - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

Quadratic Equations

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Mathematics

Find the values of k for which each of the following quadratic equation equal roots :
(i) 9x² + kx + 1 = 0
(ii) x² - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

Quadratic Equations

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Mathematics

Find the values of k for which each of the following quadratic equation equal roots :(i) 9x2 + kx + 1 = 0(ii) x2 - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

Quadratic Equations

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