Question

solve using quadratic formula \begin{gathered} {abx}^{2} + ( {b}^{2} - ac)x - bc = 0 \\ \end{gathered} abx 2 +(b 2 −ac)x−bc=0 ​ ​

Answer 1

Answer:

$ab {x}^{2} + ( {b}^{2} - ac)x - bc = 0$

Now, Using Quadratic formula,

$x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - ( {b }^{2}- ac)± \sqrt{ {({b }^{2}- ac )}^{2} - 4(ab)( - bc)} }{2ab} \\ = \frac{ac - {b}^{2}± \sqrt{({ ({b}^{2}) }^{2} + {(ac)}^{2} - 2( {b}^{2}) (ac) )+ 4a {b}^{2} c} }{2ab} \\ = \frac{ac - {b}^{2}± \sqrt{{b}^{4} + {a}^{2} {c}^{2} - 2a {b}^{2}c + 4a {b}^{2} c } }{2ab} \\ = \frac{ac - {b}^{2}± \sqrt{{b}^{4} + {a}^{2} {c}^{2} + 2a {b}^{2}c } }{2ab} \\ = \frac{ac - {b}^{2}± \sqrt{{( {b}^{2} + ac) }^{2}} }{2ab} \\ = \frac{ac - {b}^{2}± ( {b}^{2} + ac)}{2ab} \\ = \frac{ac - {b}^{2} + {b}^{2} + ac}{2ab} \: ( or) \: \frac{ac - {b}^{2} - {b}^{2} - ac}{2ab} \\ = \frac{2 ac}{2ab} \: (or) \: \frac{ - 2 {b}^{2} }{2ab} \\ = \frac{c}{b} \: (or) \: \frac{ - b}{a}$

Here's the correct answer to the question.