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If the roots of the equation x^2-2(a+b)x...

If the roots of the equation `x^2-2(a+b)x+a(a+2b+c)=0` be equal , prove that a,b, c are in G.P,

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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Short answer type question)
  1. Find the condition so that the roots of the equation a/(x-a)+b/(x-b)=5...

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  2. Show that the roots of each of the following equations are rational(a,...

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  3. Show that the roots of each of the following equations are rational(a,...

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  4. Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 ar...

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  5. If one root of the equation qx^2+px+q=0 (p,q are real) be imaginary, s...

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  6. If the roots of the equation qx^2+2px+2q=0 are real and unequal, prove...

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  7. If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove ...

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  8. If the equation x^2+px+q=0andx^2+p'x+q'=0 have a common root , prove t...

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  9. Prove that if the equations x^2+px+r=0 and x^2+rx+p=0 have a common ro...

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  10. IF x is real and the expressions 3x^2-17x+20 is always positive, show ...

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  11. Find the limits of real value of x so that the expressions 5x^2+6x-8 i...

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  12. For any real positive value of x, show that 3-xcancelgt7/(x+2).

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  13. If x is real can the value of 3+2x-x^2 be greater than 4,

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  14. If x is real can that of x^2+3x+1 less than (-5/4)?

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  15. Show that if x is real and x^2+5lt6x , then x must lie between 1 and ...

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  16. If x is real, find the real values of p which make 4x^2+px+1 always p...

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  17. IF x is real, find the real values of m which make the expressions mx-...

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  18. If ((x-5)(x^2-2x+1))/((x-7)(x^2+2x+3)) is positive for all real values...

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  19. If the equation y^2+x^2-10x+21=0 is satisfied by real values of x and ...

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  20. If x is real , show that (x-2)(x-3)(x-4)(x-5)+2 is always positive.

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