Question 1131704

Solve 6x⁴ - 35x³ + 62x² - 35x + 6 = 0
<pre>RATIONAL ROOT THEOREM produces 2 zeroes: 2 and 3. Therefore, 2 of the expression's factors are: (x - 2) and (x - 3). 
FOILing these 2 factors results in trinomial: x<sup>2</sup> - 5x + 6
Now, when 6x<sup>4</sup> - 35x<sup>3</sup> + 62x<sup>2</sup> - 35x + 6 is divided by x<sup>2</sup> - 5x + 6, we get: 6x<sup>2</sup> - 5x + 1. Factoring 6x<sup>2</sup> - 5x + 1 gives us: (3x - 1)(2x - 1).
Therefore, 6x<sup>4</sup> - 35x<sup>3</sup> + 62x<sup>2</sup> - 35x + 6 = 0 becomes: (3x - 1)(2x - 1)(x - 2)(x - 3) = 0 and the solutions are: {{{highlight_green(matrix(4,3, x, "=", highlight(1/3), x, "=", highlight(1/2), x, "=", highlight(2), x, "=", highlight(3)))}}}