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If altbltcltd the equation (x-a)(x-c)+la...

If `altbltcltd` the equation `(x-a)(x-c)+lambda(x-b)(x-d)=0` has real roots for

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If (a+b+c)>0 and a < 0 < b < c, then the equation a(x-b)(x-c)+b(x-c)(x-a)+c(x-a)(x-c)=0 has (i) roots are real and distinct (ii) roots are imaginary (iii) product of roots are negative (iv) product of roots are positive

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If p and q are odd integers the equation x^2 + 2px + 2q = 0 cannot hav...

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

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

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

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

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

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  8. Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbet...

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  9. For what values of m epsilonR, both roots of the equation x^(2)-6mx+9m...

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  10. If ax^2-bx + c=0 have two distinct roots lying in the interval (0,1); ...

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  11. The set of values of a for which the inequality, x^2 + ax + a^2 + 6a ...

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  12. Find all integral values of a for which the quadratic expression (x - ...

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  13. Find the values of the parameter a for which 4^x-a.2^x-a+3 <= 0 for at...

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  14. Find all values of the parameter a for which the inequality a.9^x +4(a...

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  15. Solve the equation sqrt(a(2x^x-2)+1)=1-2^x ,x in Rdot

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  16. Find the possible values of 'a' such that the inequality 3-x^(2)gt ...

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  17. The sum of all the integral value(s) of k in [0, 15] for which the ine...

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  18. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

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  19. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

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  20. If f(x)=x^2+b x^2+c x+da n df(0),f(-1) are odd integers, prove that f(...

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