Question

the roots of the equation x^4-8x^2-9=0​

Answer 1

Answer:

please refer to the attachment

Answer 2

The roots of the equation are -3,3,i,-i.

Step-by-step explanation:

Given : Equation $x^4-8x^2-9=0$

To find : The roots of the equation ?

Solution :

Equation $x^4-8x^2-9=0$

Applying middle term split,

$x^4-9x^2+x^2-9=0$

$x^2(x^2-9)+1(x^2-9)=0$

$(x^2-9)(x^2+1)=0$

Applying algebraic identity, $a^2-b^2=(a+b)(a-b)$

$(x+3)(x-3)(x^2+1)=0$

Applying zero product property, $a\cdot b=0\Rightarrow a=0,b=0$

$x+3=0\\\Rightarrow x=-3$

or

$x-3=0\\\Rightarrow x=3$

or

$x^2+1=0\\\Rightarrow x=\pm\sqrt{-1}=\pm\ i$

Therefore, the roots of the equation are -3,3,i,-i.

#Learn more

If the sum of the roots of the equation kx2-2√2x+1=0, is√2,then find the roots of the equation.

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