Question

find the value of k pls ​

Answer 1

Answer:

$b \: \: \: ( - \frac{4}{7} ,4)$

Step-by-step explanation:

$for \: \: a {x}^{2} + bx + c = 0 \\ \\ to \: have \: distinct \: roots \\ \\ {b}^{2} - 4ac > 0 \\ \\ here \\ \\ a = 2k + 1 \\ b = - (7k + 2) \\ c = 7k - 3 \\ \\ = > ( - (7k + 2)) {}^{2} - 4(2k + 1)(7k - 3) > 0 \\ \\ = > 49 {k}^{2} + 28k + 4 - (56 {k}^{2} + 4k - 12) > 0 \\ \\ = > - 7 {k}^{2} + 24k + 16 > 0 \\ \\ = > 7 {k}^{2} - 24k - 16 < 0 \\ \\ = > 7 {k}^{2} - 28k + 4k - 16 < 0 \\ \\ = > 7k(k - 4) + 4(k - 4) < 0 \\ \\ = > (7k + 4)(k - 4) < 0 \\ \\ = > x < < > > ( - \frac{4}{7} \: ,\: 4)$

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