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If alpha,beta,gamma be the roots of ax^3...

If `alpha,beta,gamma` be the roots of `ax^3+bx^2+cx+d=0` then find the value of `sum 1/alpha`.

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. Solve the equation 24x^3-14x^2-63x + alpha= 0, one root being double ...

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  2. If alpha,beta,gamma be the roots of ax^3+bx^2+cx+d=0 then find the val...

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  3. If alpha,beta,gamma be the roots of ax^3+bx^2+cx+d=0 then find the val...

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  4. If alpha,beta,gamma are the roots of the equation ax^3+bx^2+cx+d=0 the...

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

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  6. Find the sum of all the values of m so that , the equations 3x^(2)-2mx...

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  7. Prove that equations (q-r)x^2 + (r-p)x + p-q = 0 and (r-p)x^2+(p-q)x+q...

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  8. Prove that , if the equations x^2+bx+ca=0 and x^2+cx+ab=0 have only no...

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  9. If the two equation x^(2)-cx+d=0 and x^(2)-ax+b=0 have one common root...

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  10. If ax^2+2bx+c=0 and a1x^2=2b1x+c1=0 have commonroot and a/a1,b/b1,c/c1...

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  11. If equations ax^(2)-bx+c=0 (where a,b,c epsilonR and a!=0) and x^(2)+2...

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  12. If a,b,c, a1,b1,c1 are rational and equations ax^2+2bx+c=0 and a1x^2+2...

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  13. If the equation x^2+ax+12=0 , x^2 +bx +15 =0 and x^2 (a+ b) x+ 36 =0 ...

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  14. Let lambda,mu be such that the equations 4x^2 - 8x + 3 = 0, x^2 + lamb...

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  15. Find the values of a for which x^2-ax+1-2a^2ge0 for real values of x.

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  16. Find the minimum value of 3x^2-6x+7, x in R and also find the correspo...

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  17. Find the maximum value of (2+3x)(1-x),x in R and also find the corresp...

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  18. If f(x) = (x^2 -2x + 4)/(x^2+2x+4), x in R then range of function is

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  19. Range of (x^2-x+1)/(x^2+x+1) is

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  20. If for all real x (x+a)/(x^2+b x+c^2) cannot lie between two limits, ...

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