Reducible method of chapter quadratic equation.

Given: Reducible method

To explain: Here we have to explain reducible method.

Solution:

Let say we have an equation:

 $x^{4} \ –\ 10x^{2} \ +\ 9\ =\ 0$

The equation can be re-written as $x^{4} \ –\ x^{2} \ –\ 9x^{2} \ +\ 9\ =\ 0$.

 Next, we get  $x^{2}\left( x^{2} \ -\ 1\right) \ –\ 9\left( x^{2} \ -\ 1\right) \ =\ 0$, which finally gives us  $\left( x^{2} \ -\ 1\right)\left( x^{2} \ -\ 9\right) \ =\ 0$.

Now, equating both factors to zero gives $x^{2} \ =\ 1$ and $x^{2} \ =\ 9$.

From these two equations, we get four solutions: $1,\  –1,\  3,\  and\  –3$.

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Updated on: 10-Oct-2022

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