1.

Find the values of k for which the given quadratic equation has real and distinct roots: (i)` kx^(2)+6x+1=0" "(ii)" "x^(2)-kx+9=0` (iii)` 9x^(2)+3kx+4=0" "(iv)" "5x^(2)-kx+1=0`

Answer» Correct Answer - (i)` klt9" "(ii)" "kgt6" or "klt-6" "(iii)" "kgt4" or "klt-4" "(iv)" "kgt2sqrt(5)" or "klt-2sqrt(5)`
(i) `36-4kgt0implies36gt4kimplies4klt36impliesklt9.`
(ii) `k^(2)-36gt0impliesk^(2)gt36implieskgt6" or "klt-6.`
(iii) `9k^(2)-144gt0impliesk^(2)gt16implieskgt4" or "klt-4.`
(iv)` k^(2)-20gt0impliesk^(2)gt20implieskgt2sqrt(5)" or "klt-2sqrt(5).`


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