Which of the following denotes the ratio of the sum and the product of the roots of $5 x^{2} - 14 x + 8 = 0$ ?

7:4

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8 : 9

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14 : 5

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8 : 5

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Solution

The correct option is A
7:4

For, $5 x^{2} - 14 x + 8 = 0$

Sum of the roots = $- \frac{(- 14)}{5} = \frac{14}{5}$

Product of the roots = $\frac{8}{5}$

Thus, sum of roots : product of roots = $\frac{14}{5} : \frac{8}{5} = 14 : 8 = 7 : 4$

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[Ratio in its reduced form]

\sqrt{5 x^{2} - 6 x + 8} - \sqrt{5 x^{2} - 6 x - 7} = 1

\sqrt{5 x^{2} - 6 x + 8} - \sqrt{5 x^{2} - 6 x - 7} = 1

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