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If \(\alpha, \beta\) are the roots of equation 18 + 15x - 3x2 = 0, find \({\alpha}\beta - {\alpha}-\beta \)...


Question

If \(\alpha, \beta\) are the roots of equation 18 + 15x - 3x2 = 0, find \({\alpha}\beta - {\alpha}-\beta \)

Options

A) 11

B) -11

C) 10

D) -10

The correct answer is B.

Explanation:

\(18 + 15x - 3x^2 = 0\)
\(a = - 3, b = 15, c = 18\)
\(\alpha +\beta =\frac{-b}{a}=\frac{-15}{-3}=5\)
\(\mathit{\alpha \beta }=\frac c a=\frac{18}{-3}=-6\)
\(\mathit{\alpha \beta }-\alpha -\beta =\mathit{\alpha \beta }-\left(\alpha +\beta \right)\)
\(= -6 - (5) = - 11\)

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Dicussion (1)

  • \(18 + 15x - 3x^2 = 0\)
    \(a = - 3, b = 15, c = 18\)
    \(\alpha +\beta =\frac{-b}{a}=\frac{-15}{-3}=5\)
    \(\mathit{\alpha \beta }=\frac c a=\frac{18}{-3}=-6\)
    \(\mathit{\alpha \beta }-\alpha -\beta =\mathit{\alpha \beta }-\left(\alpha +\beta \right)\)
    \(= -6 - (5) = - 11\)

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