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  4. If the roots α, β of the quadratic equation ( sin 6+ sin 10+ cos 10) x2+x+k2-3 k+2=0, is such that α<0<β, then the true set of values of k is,

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Q. If the roots $\alpha, \beta$ of the quadratic equation $(\sin 6+\sin 10+\cos 10) x^2+x+k^2-3 k+2=0$, is such that $\alpha<0<\beta$, then the true set of values of $k$ is,

Complex Numbers and Quadratic Equations

Solution:

$\text { Note: } \sin 6+\sin 10+\cos 10<0 $
$\text { So, } f(0)>0 \Rightarrow (k-1)(k-2)>0 $
$\Rightarrow k \in(-\infty, 1) \cup(2, \infty)$

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