Question

Determine the quadratic equations whose sum and product of roots are
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Answer 1

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Given the roots of the quadratic equation are $\frac{5}{3}$ and 4

Let, $\alpha = \frac{5}{3} \: and \: \beta = 4$

We know the formula when roots are given, $x²-(\alpha+ \beta) x+(\alpha\beta)$ is the equation.

${x}^{2} - {(} \frac{5}{3} + 4)x + (\frac{5}{3} )(4) = {x}^{2} - \frac{17}{3} x + \frac{20}{3} \\ \frac{ {3x}^{2} - 17x + 20 }{3} = 0 \\ {3x}^{2} - 17x + 20 = 0$

Therefore the equation is 3x² - 17x +20.