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If the difference between the roots of the equation `x^2+""a x""+""1""=""0` is less than `sqrt(5)` , then the set of possible values of a is (1) `(-3,""3)` (2) `(-3,oo)` (3) `(3,oo)` (4) `(-oo,-3)`

A

`(-3,3)`

B

`(-3,oo)`

C

`(3,oo)`

D

`(-oo,-3)`

Text Solution

Verified by Experts

`alpha+beta=-a`
`|alpha-beta|ltsqrt(5)implies(alpha-beta)^(2)lt5`
`impliesa^(2)-4lt5impliesa epsilon(-3,3)`
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JEE MAINS PREVIOUS YEAR-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  3. The conjugate of a complex number is 1/(i-1) . Then the complex num...

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  4. The quadratic equations x^2"-"6x""+""a""=""0""a n d""x^2"-"c x""+""...

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  5. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, ...

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  6. If |z-4/z|=2 , then the maximum value of |Z| is equal to (1) sqrt(3...

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  7. If alpha and beta are the roots of the equation x^2"-"x""+""1""=""0 , ...

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  8. The number of complex numbers z such that |z""""1|""=""|z""+""1|""=""|...

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  9. Let alpha,beta be real and z be a complex number. If z^2+alphaz""+beta...

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  11. If z!=1 and (z^2)/(z-1) is real, then the point represented by the ...

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  12. If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R have a comm...

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  14. The real number k for which the equation, 2x^3+""3x""+""k""=""0 has tw...

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  15. Let a and b be the roots of equation p x^2+q x+r=""0, p!=0. . If p, q,...

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  16. If z is a complex number such that |z|>=2 then the minimum value of |z...

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  17. A complex number z is said to be unimodular if . Suppose z1 and z2 a...

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  18. Let alpha and beta be the roots of equation x^2-6x-2""=""0 . If an=...

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  19. A value of theta for which (2+3isintheta)/(1-2isintheta) purely imagi...

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