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Show that 1 is a root of a(b-c)x^2+b(c-a...

Show that 1 is a root of `a(b-c)x^2+b(c-a)x+c(a-b)=0`.Hence show that if roots of this equation are equal then 1/a,1/b,1/c are in A.P.

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UNITED BOOK HOUSE-THE SCOTTISH CHURCH COLLEGIATE SCHOOL-EXERCISE
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  2. For all n ge 1 prove that (1)/(1.2)+ (1)/(2.3)+(1)/(3.4)+.....+(1)/...

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  3. Show that 1 is a root of a(b-c)x^2+b(c-a)x+c(a-b)=0.Hence show that if...

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  4. Find the sum to n terms :1/2+3/2^2+5/2^3+...+(2n-1)/2^n

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  5. Find the term inedpendent of X in the expansion of (1+x)^3(1-1/x)^6

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  6. A moving st.line always passes through a fixed pt.(alpha,beta).Prove t...

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  7. Find the image of the pt.(-3,-1)with respect to the st.line 2x+3y+22=0

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  8. Find equations of all possible circles that touch the y axis at the po...

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  9. Find the equation of the circles which touche the y axes id and passes...

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  10. Show that lim(xrarr1)(1-x)tan((pix)/2)=2/pi

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  11. If 2f(x)+3f(-x)=x^2-x-1,then find f'(1).

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  12. Find from the first principle,the derivative of tan 2x at x=pi/8

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  13. If f(x) is differentiable at x=a then show that lim(xrarr0)(x^2f(a)-a^...

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  14. Prove the following by contradiciton ."The sum of a rational and an ir...

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  15. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  16. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  17. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  18. Let a statement p:/\ABCis right angle triangle,and another statement q...

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  19. Find the range of the function f(x)=1/(3sinx+4cosx+6)

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  20. Prove thatcos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

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