Question

Plz answer this question really i will mark the answer as brainlist
In this question u have to find value of K for which given equation has real and equal roots

Answer 1

For a quadratic equation, roots are real and equal if it's discriminant is 0
${(2(1 + 3k))}^{2} - 4 \times 1 \times 7(3 + 2k) = 0 \\ 4(1 + 6k + 9 {k}^{2} ) - 28(3 + 2k) = 0 \\ 36 {k}^{2} - 32k - 80 = 0 \\ 9 {k}^{2} - 8k - 20 = 0 \\ k = \frac{8 + \: or \: - \sqrt{ { - 8}^{2} - 4 \times 9 \times - 20} }{2 \times 9} \\ k = \frac{8 + \: or \: - 28}{18} \\ k = \frac{36}{18} \: \: or \: \: \frac{ - 20}{18} \\ k = 2 \: \: or \: \: \frac{ - 10}{9}$