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If [x] and (x) are the integral part of ...

If `[x]` and `(x)` are the integral part of x and nearest integer to `x` then solve `(x)[x]=1`

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CaseI If `x epsilonI`, then `x=[x]=(x)`
`:.` Given equation convert in `x^(2)=1`
`:.x=(+-1)`
Case II If `x!inI` then `(x)=[x]+1`
`:.` Given equation convert in
`([x]+1)[x]=1implies[x]^(2)+[x]-1=0`
or `[x]=(-1+-sqrt(5))/2` [impossible]
Then final answer is `x=+-1`.
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ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

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  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

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  4. If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c ...

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  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

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  6. If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are ...

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  7. Let a and b be the roots of the equation x^2-10 c x-11 d=0 and those ...

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  8. Let a,b,c be the sides of a triangle. No two of them are equal and lam...

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  9. All the value of m for which both the roots of the equation x 2 −2mx...

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  10. If the roots of the quadratic equation x^2+p x+q=0 are tan30^0a n dtan...

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  11. Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2...

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  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

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  13. Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots o...

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

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  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

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  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

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  17. Find the discriminant of the quadratic equation 2x^2-4x+3=0, and hence...

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

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  19. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

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  20. solve 0=-1+2x+3x^2

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  21. Find the roots of x^2-6x-2=0

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