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Prove that for any value of a, the inequ...

Prove that for any value of a, the inequatiion `(a^(2)+3)x^(2)+(a+2)x-6lt0` is true for atleast one negative `x`.

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We have `(a^(2)-3)x^(2)+(a+2)x-6lt0`

Let `f(x)=(a^(2)+3)x^(2)+(a+2)x-6`
`(a^(2)+3)gt0` and `f(x)lt0`
`:.Dgt0`
`implies(a+2)^(2)+24(a^(2)+3)gt0` is true for all `a epsioonR`
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ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Subjective Type Questions)
  1. If one root of the equation ax^2 + bx + c = 0 is equal to the n^(th) p...

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  2. If alpha, beta be the roots of the equation ax^2 + bx + c= 0 and gamma...

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  3. Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)...

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  4. If the equation x^(2)-px+q=0 and x^(2)-ax+b=0 have a comon root and th...

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  5. If the equation x^(2)-2px+q=0 has two equal roots, then the equation (...

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  6. Solve the equation x^(log(x)(x+3)^(2))=16.

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  7. Solve the equation (2+sqrt(3))^(x^(2)-2x+1)+(2-sqrt(3))^(x^(2)-2x-1)=...

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  8. Solve the equation x^(2)+(x/(x-1))^(2)=8

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  9. Find number of solutions of the equation sqrt((x+8)+2sqrt(x+7))+sqrt((...

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  10. Find value of x if x^2+5|x|+6=0

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  11. Solve x^(2)+2x-3

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  12. Solve the system x^(2)-2|x|=0

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  13. If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 ...

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  14. If A(1),A(2),A(3),...,A(n),a(1),a(2),a(3),...a(n),a,b,c in R show that...

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  15. One root of the quadratic equation x^(2)-12x+a=0 is thrice the other....

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  16. If [x] is the integral part of a real number x. Then solve [2x]-[x+1]=...

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  17. Prove that for any value of a, the inequatiion (a^(2)+3)x^(2)+(a+2)x-6...

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  18. How many real solutions of the equation 6x^(2)-77[x]+147=0, where [x] ...

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  19. If alpha, beta are the roots of the equation x^(2)-2x-a^(2)+1=0 and ga...

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  20. If the equation x^(4)+px^(3)+qx^(2)+rx+5=0 has four positive real root...

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