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If each pair of the three equations x^(2...

If each pair of the three equations `x^(2)+ax+b=0, x^(2)+cx+d=0` and `x^(2)+ex+f=0` has exactly one root in common then show that `(a+c+e)^(2)=4(ac)+ce+ea-b-d-f`

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The correct Answer is:
`=4(ac+ce+ea-b-d-f)`
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MOTION-QUADRATIC EQUATION-EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)
  1. If each pair of the three equations x^(2)+ax+b=0, x^(2)+cx+d=0 and x^(...

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  2. If the difference between the roots of the equation x^2+""a x""+""1...

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  3. The quadratic equations x^2""6x""+""a""=""0""a n d""x^2""c x""+""6"...

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  4. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

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  5. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, ...

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  6. If a and b are the roots of the equation x^2""x""+""1""=""0 , then alp...

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  7. 8. Sachin and Rahul attempted to solve a quadratic equation. Sachin ma...

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  8. Show that the equation e^(sinx)-e^(-sinx)-4=0 has no real solution.

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  9. The real number k for which the equation, 2x^3+""3x""+""k""=""0 has tw...

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  10. If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R have a comm...

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  11. Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != ...

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  12. If a in R and the equation -3(x-[x])^2+2(x-[x])+a^2=0 (where [x] denot...

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  13. Let alpha and beta be the roots of equation x^2-6x-2""=""0 . If an=...

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  14. alpha,beta be the roots of the equation x^2-px+r=0 and alpha/2 , 2beta...

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  15. Let f(x)=(x^(2)-6x+5)/(x^(2)-5x+6) Match the expressions/ statements i...

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  16. Let a,b,c,p,q be the real numbers. Suppose alpha,beta are the roots of...

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  17. The smallest value of k, for which both the roots of the equation, x^2...

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  18. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

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  19. Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if an=al...

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  20. A value of b for which the equation x^2+b x-1=0,x^2+x+b=0 have one roo...

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  21. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

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