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Roots of a Quadratic Equation

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Question

Find the roots of the equation $5 x^{2} - 7 x - 6 = 0$

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Solution

The equation is
$5 x^{2} - 7 x - 6 = 0$

$\Rightarrow 5 x^{2} + 3 x - 10 x - 6 = 0$

$\Rightarrow x (5 x + 3) - 2 (5 x + 3) = 0$

$\Rightarrow (x - 2) (5 x + 3) = 0$

$\Rightarrow x = 2, \frac{- 3}{5}$

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Q. Find the roots of the following quadratic equations, if they exist

5 x^{2} - 7 x - 6 = 0

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5 q^{2} - 7 q - 3 = 0

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5 x^{2} - 7 x + 2 = 0 ?

Q. If the roots of the equation

5 x^{2} - 7 x + k = 0

are mutually reciprocal then

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