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Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 - 5x + 3. Compute a^3*b + a*b^3.

 Dec 6, 2022
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First, you simplify the sides, pretty straightforward you get x^2 - 3x + 4. Keep in mind that the sum of the roots = -b/a and the product of the roots = c/a. I will put r_1 as a, and r_2 as b. so a + b = -3, and ab = 4. Solve the systems and sub in for a^3 * b + a* b^3

 Dec 6, 2022

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