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# help

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The roots of the quadratic equation 3x²-kx+14=0 are in the ratio 7:6, then k equals?

Jun 24, 2020

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This means that

$$\begin{cases}\text{sum of roots} = \dfrac k3\\\text{product of roots} = \dfrac{14}3\end{cases}$$

Let the roots be 7p and 6p. Using the second formula,

$$(7p)(6p) = \dfrac{14}3\\ p^2 = \dfrac19\\ p = \pm \dfrac13$$

Using the first formula,

$$13p = \dfrac k3\\ k = 39p = \pm13$$

Jun 24, 2020