If the difference between the roots of the equation x2-ax-1-0 is less than -5- then which of the following can be the possible values of a -

Let p,q be the roots of the equation nbsp;x^2+ax+1=0 and nbsp; |p q| lt;√(5) p+q= a, p× q=1 ⇒√((p+q)^2 4pq) lt;√(5) ⇒√(a^2 4) lt;√(5) ⇒ a^2 4 lt;5 ...

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Standard XI

Mathematics

Relations Between Roots and Coefficients

If the differ...

Question

If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ is less than $\sqrt{5}$ , then which of the following can be the possible values of $a$ ?

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Solution

The correct option is C $1$
Let $p, q$ be the roots of the equation $x^{2} + a x + 1 = 0$ and
$| p - q | < \sqrt{5}$
$p + q = - a, p \times q = 1$

$\Rightarrow \sqrt{(p + q)^{2} - 4 p q} < \sqrt{5}$

$\Rightarrow \sqrt{a^{2} - 4} < \sqrt{5}$
$\Rightarrow a^{2} - 4 < 5$
$\Rightarrow a^{2} < 9$
$\Rightarrow - 3 < a < 3$
$∴ a \in (- 3, 3)$

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If the difference between the roots of the equation x2+ax+1=0 is less than √5, then which of the following can be the possible values of a ?

The correct option is C 1Let p,q be the roots of the equation x2+ax+1=0 and |p−q|<√5 p+q=−a,p×q=1 ⇒√(p+q)2−4pq<√5 ⇒√a2−4<√5 ⇒a2−4<5 ⇒a2<9 ⇒−3<a<3 ∴a∈(−3,3)

If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ is less than $\sqrt{5}$ , then which of the following can be the possible values of $a$ ?