Question

If Alpha And Beta Are The Zeros Of The Polynomial 6x2+x-2 Then Find The Value Of Alpha Square + Beta Square

Answer 1

Answer:

the answer is 25/36.

refer to the above attachment for the solution.

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Answer 2

Step-by-step explanation:

${6x}^{2} + x - 2 = 0 \\ {6x}^{2} + 4x - 3x - 2 = 0 \\ 2x(3x + 2) - 1(3x + 2) = 0 \\ (2x - 1)(3x + 2) = 0 \\ either \: \\ 2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2} \ \\ \alpha = \frac{1}{2} \\ or \\ 3x + 2 = 0 \\ 3x = - 2 \\ x = \frac{ - 2}{3 } \\ \beta = \frac{ - 2}{3} \\ now \\ { \alpha }^{2} + { \beta }^{2} \\ = {( \frac{1}{2}) }^{2} + { (\frac{ - 2}{3} )}^{2} \\ = \frac{1}{4} + \frac{4}{9} \\ = \frac{9 + 16}{36} \\ = \frac{25}{36}$