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If a, b, c are in GP, then the equations...

If `a, b, c` are in `GP`, then the equations `ax^2 +2bx+c = 0` and `dx^2 +2ex+f =0` have a common root if `d/a , e/b , f/c `are in

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

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  2. 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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  3. If a, b, c are in GP, then the equations ax^2 +2bx+c = 0 and dx^2 +2ex...

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  4. Show that the minimum value of (x+a)(x+b)//(x+c)dotw h e r ea > c ,b >...

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  5. Find the values of a for which the expression (ax^2+3x-4)/(3x-4x^2+a) ...

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  6. If |(12x)/(4x^(2)+9)| le 1, then

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  7. Prove that for all real values of xa n dy ,x^2j+2x y+3y^2-6x-2ygeq-11.

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  8. The value(s) of m for which the expression 2x^2+mxy+3y^2-5y-2 can be ...

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  9. if alpha is a real root of the quadratic equation ax^2+bx+c=0 and beta...

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  10. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

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  11. If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has at...

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  12. For what values of a the following will be an identity in x ? (x^2-1)a...

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  13. The number of integral triplets (a, b, c) such thet a+b cos 2x+c sin^(...

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  14. Let k be the value of a for which the equation (a^2 + 4a + 3) x^2 + (a...

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  15. Solve (x^2+2)^2+8x^2=6x(x^2+2)

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  16. Solve (x+4)(x+7)(x+8)(x+11)+20=0.

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  17. Solve sqrt(5x^2-6x+8)+sqrt(5x^2-6x-7)=1.

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  18. Number of real solutions of sqrt(x)+sqrt(x-sqrt(1-x))=1 is

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  19. Solve (x+3)^4+(x+2)^4+(x+1)^4 = 98.

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  20. Solve for x : 2x^3+5x^2-2x+3 = 0.

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