Many polynomial equations need significant rearrangement before they are in a form…

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Many polynomial equations need significant rearrangement before they are in a form suitable for the polynomial solver on a calculator. For example, consider (x−4)(x2−1)=(2−x2)(x+1)(x - 4)(x^2 - 1) = (2 - x^2)(x + 1). (1) What are the advantages and disadvantages of: - ▶ rearranging the equation using algebra and hence using the polynomial solver - ▶ graphing both sides of the equation on the same set of axes then finding the xx -coordinates of any points of intersection? (2) How reliable is technology? For example, can you use your calculator to solve: - ▶ xx=−1x^x = -1 - ▶ (x2−2)2(70x−99)=0(x^2 - 2)^2(70x - 99) = 0 ?

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