Find the values of k for which each of the following quadratic equation has equal roots : (i) x 2 + 4kx + (k 2 - k + 2) = 0 (ii) (k - 4)x 2 + 2(k - 4)x + 4 = 0

(i) The given equation is x 2 + 4kx + (k 2 - k + 2) = 0. Comparing with ax 2 + bx + c = we obtain, a = 1 , b = 4k , c = (k 2 - k + 2) For equal roots, discriminant = 0 Hence, the value of k is -1, . (ii) The given equation is (k - 4)x 2 + 2(k - 4)x + 4 = 0. Comparing with ax 2 + bx + c = we obtain, a = k - 4 , b = 2(k - 4) , c = 4 For equal roots, discriminant = 0 k ≠ 4 , as that will make a = (k - 4) = 0 and thus roots will become = ∞ . Hence, the value of k is 8.

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Without solving the following quadratic equations, find the value of 'p' for which the given equations have real and equal roots :
(i) px² - 4x + 3 = 0
(ii) x² + (p - 3)x + p = 0

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Find the value(s) of m for which each of the following quadratic equation has real and equal roots :
(i) (3m + 1)x² + 2(m + 1)x + m = 0
(ii) x² + 2(m - 1)x + (m + 5) = 0

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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.

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Mathematics

Find the values of k for which each of the following quadratic equation has equal roots :
(i) x² + 4kx + (k² - k + 2) = 0
(ii) (k - 4)x² + 2(k - 4)x + 4 = 0

Quadratic Equations

Related Questions

Without solving the following quadratic equations, find the value of 'p' for which the given equations have real and equal roots :
(i) px² - 4x + 3 = 0
(ii) x² + (p - 3)x + p = 0

Find the value(s) of m for which each of the following quadratic equation has real and equal roots :
(i) (3m + 1)x² + 2(m + 1)x + m = 0
(ii) x² + 2(m - 1)x + (m + 5) = 0

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.

Mathematics

Find the values of k for which each of the following quadratic equation has equal roots :(i) x2 + 4kx + (k2 - k + 2) = 0(ii) (k - 4)x2 + 2(k - 4)x + 4 = 0

Quadratic Equations

Related Questions

Without solving the following quadratic equations, find the value of 'p' for which the given equations have real and equal roots :(i) px2 - 4x + 3 = 0(ii) x2 + (p - 3)x + p = 0

Find the value(s) of m for which each of the following quadratic equation has real and equal roots :(i) (3m + 1)x2 + 2(m + 1)x + m = 0(ii) x2 + 2(m - 1)x + (m + 5) = 0

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.

Find the values of k for which each of the following quadratic equation has equal roots :
(i) x² + 4kx + (k² - k + 2) = 0
(ii) (k - 4)x² + 2(k - 4)x + 4 = 0

Without solving the following quadratic equations, find the value of 'p' for which the given equations have real and equal roots :
(i) px² - 4x + 3 = 0
(ii) x² + (p - 3)x + p = 0

Find the value(s) of m for which each of the following quadratic equation has real and equal roots :
(i) (3m + 1)x² + 2(m + 1)x + m = 0
(ii) x² + 2(m - 1)x + (m + 5) = 0

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.