Let $x^{2} + α x + β = 0$ be the equation whose roots are the negatives of the roots of $x^{2} + 7 x - 2 = 0$ , then the value of $α + β$ is

5

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- 5

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9

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- 9

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Solution

The correct option is D $- 9$
Let $x_{1}, x_{2}$ be the roots of the equation $x^{2} + 7 x - 2 = 0$
$\Rightarrow x_{1} + x_{2} = - 7, & x_{1} \times x_{2} = - 2$
So,
$- x_{1}, - x_{2}$ are the roots of the equation
$x^{2} + α x + β = 0$
$- (x_{1} + x_{2}) = 7 = - α \Rightarrow α = - 7 \Rightarrow β = (- x_{1}) (- x_{2}) = x_{1} \times x_{2} = - 2 \Rightarrow α + β = - 9$

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