Question

Solve the equation and express each solution in a+bi form . X^4-44x^2-45=0

Answer 1

Answer:

The correct answer is option

$d.\ x=-i, i, 3 \sqrt{5}\ or\ -3 \sqrt{5}$

Step-by-step explanation:

The given equation has a degree 4  (Highest power of $x$):

$x^4-44x^2-45=0$ is the given equation which can be written as:

$(x^2)^2-44x^2-45=0 ...... (1)$

Let $t=x^{2}$ and putting it in equation (1):

$t^2-44t-45=0$

Solving the above quadratic equation in variable $t$:

$\Rightarrow t^2-45t+t-45=0 \\\Rightarrow t(t-45)+1(t-45)=0\\\Rightarrow (t+1)(t-45)=0\\\Rightarrow t =-1\ or\ 45$

We know that $t=x^{2}$

So, $x^{2} =-1\ or\ x^{2}= 45$

1. Solving $x^{2} =-1$

$\Rightarrow x = +\sqrt{-1}\ or\ -\sqrt{-1}\\\Rightarrow x = i\ or\ -i$

2. Solving $x^{2} =45$

$\Rightarrow x = +\sqrt{45}\ or\ -\sqrt{45}\\\Rightarrow x = 3\sqrt{5}\ or\ -3\sqrt{5}$

Hence, correct answer is:

$x=-i, i, 3 \sqrt{5}\ or\ -3 \sqrt{5}$

Answer 2

Answer:

D

Step-by-step explanation:

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