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Find the set of all real 'a' such that `5a^(2)-3a-2,a^(2)+a-2` and `2a^(2)+a-1` are the lenghts of the sides of a triangle?

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. Solve the equations log1000 |x+y| = 1/2 . log10 y - log10 |x| = log100...

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  2. Find all values of theta in the interva (-pi/2,pi/2) satisfying the eq...

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  3. Find the set of all real 'a' such that 5a^(2)-3a-2,a^(2)+a-2 and 2a^(2...

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  4. Solve (x+3)^(2)-(x-1)^(5)ge244.

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  5. Let sqrt(((x+1)(x-3))/((x-2))). Find all the real values of x for whic...

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  6. Let f(x)= (2x)/(2x^2+5x+2) and g(x)=1/(x+1). Find the set of real valu...

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  7. 1 < (3 x^2 - 7x + 8)/(x^2 + 1) <2

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  8. Solve for x in R : 4^(x^2)=< 3.2^(x^2+2)+ 4^(x+1).

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  9. Solve abs(x-1) + abs(x-2) + abs(x-3)ge 6, x in R.

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  10. Solve abs(abs(x-2)-1) ge 3.

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  11. If x=4/9 satisfies the equation (log)a(x^2-x+2)>(log)a(-x^2+2x+3), the...

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  12. If log(3x+5)(a x^2+8x+2)>2 then x lies in the interval

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  13. Let there be a quotient of two natural numbers in which the derin whic...

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  14. If p and q are odd integers the equation x^2 + 2px + 2q = 0 cannot hav...

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  15. If the roots of x^2-ax+b=0 are real and differ by a quantity which is ...

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  16. If altbltcltd the equation (x-a)(x-c)+lambda(x-b)(x-d)=0 has real root...

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  17. If p is the first of the n arithmetic means between two numbers and q ...

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  18. Let a ,b in na n a > 1. Also p is a prime number. If a x^2+b x+c=p fo...

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  19. Given two quadratic equation x^2-x+m=0 and x^2-x+3m=0, m!=0. Find the ...

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  20. If a, b, c are in HP, find the relation between the roots of ax^2+bx+c...

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