Question

If roots $\alpha$ and $\beta$ of the equation $x^2+px+q=0$ are such that $3\alpha +4\beta =7$ and $5\alpha -\beta =4$, then $(p,q)$ is equal to

• A. $(1,1)$
• B. $(-1,1)$
• C. $(-2,1)$
• D. $(2,1)$

Answer 1

The correct option is A $(1,1)$

$3\alpha +4\beta =\mathrm{7.....}\left(i\right)$

$5\alpha -\beta =\mathrm{4.......}\left(ii\right)$

$3\alpha +4\beta =7$

$20\alpha -4\beta =16$

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$23\alpha =23$

$\therefore$ $\alpha =1$

$\beta =1$

$\alpha +\beta =-p$

$\Rightarrow$ $p=-2$

$\alpha \beta =q$

$\Rightarrow$ $q=1$

$(p,q)=(-2,1)$