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solve this equation :-

4k³+ 18k² + 23k + 9 =0 (step by step)

$4 k^{3} + 18 k^{2} + 23 k + 9 = 0 \Rightarrow 4 k^{3} + 4 k^{2} + 14 k^{2} + 14 k + 9 k + 9 = 0 \Rightarrow 4 k^{2} (k + 1) + 14 k (k + 1) + 9 (k + 1) = 0 \Rightarrow (k + 1) (4 k^{2} + 14 k + 9) = 0 \Rightarrow k = - 1 o r 4 k^{2} + 14 k + 9 = 0 ...... (1) N o w, f a c t o r o f 4 k^{2} + 14 k + 9, U \sin g S r i d h a r a c h a r y a m e t h o d, w e h a v e, k = \frac{- 14 \pm \sqrt{{(14)}^{2} - 4 \times 4 \times 9}}{2 \times 4} = \frac{- 14 \pm \sqrt{52}}{8} = \frac{- 7 \pm \sqrt{13}}{4} H e n c e, k = - 1, \frac{- 7 + \sqrt{13}}{4}, \frac{- 7 - \sqrt{13}}{4}$

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