Theory Of Equations Ques 4
- For all ’ $x^{\prime}, x^2+2 a x+(10-3 a)>0$, then the interval in which ’ $a$ ’ lies is
(2004, 1M)
(a) $a<-5$
(b) $-5<a<2$
(c) $a>5$
(d) $2<a<5$
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Answer:
Correct Answer: 4.(b)
Solution: (b) As we know, $a x^2+b x+c>0$ for all $x \in R$, iff $a>0$ and $D<0$.
Given equation is $x^2+2 a x+(10-3 a)>0, \forall x \in R$
Now,
$ D<0 $
$\Rightarrow \quad 4 a^2-4(10-3 a)<0 $
$\Rightarrow \quad 4\left(a^2+3 a-10\right)<0 $
$\Rightarrow \quad (a+5)(a-2)<0 \Rightarrow a \in(-5,2)$
BETA
