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Solve the polynomial equation by factoring: x^4 +100 = 29x^2

Question:

Solve the polynomial equation by factoring:

{eq}x^4 +100 = 29x^2 {/eq}

Polynomials:

Polynomials are the expressions containing a single independent variable that is related by various mathematical operations like addition, subtraction, multiplication, etc..

Generally, a polynomial is in the form {eq}\displaystyle a_0 x^n+a_1 x^{n-1} +a_2 x^{n-2} +a_3 x^{n-3}+......... +a_n {/eq}

"n" is called the degree of the polynomial.

Answer and Explanation:

Given, polynomial equation

{eq}\displaystyle x^4+100=29x^2 {/eq}

Solving the given equation

{eq}\displaystyle \begin{align} x^4+100 &= 29x^2 \\ x^4 -29x^2+100 &= 0 \\ x^4 -4x^2-25x^2+(25)(4) &= 0 &&\text{[Converting -29 as the sum of -25,-4.]} \\ x^2(x^2-4)-25(x^2-4) &= 0 &&\text{[Taking} \ x^2 \text{common as well as -25]} \\ (x^2-25)(x^2-4) &= 0 \\ \implies x &= \pm 5 \ or \ \pm 2 \end{align} {/eq}

The solution to the given equation is {eq}\displaystyle x = \pm 5 \ or \ \pm 2 {/eq}


Learn more about this topic:

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