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Prove that equations (q-r)x^2 + (r-p)x +...

Prove that equations `(q-r)x^2 + (r-p)x + p-q = 0` and `(r-p)x^2+(p-q)x+q-r=0` have a common root.

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The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

If p, q, r are in G.P. and the equations, p x^2+2q x+r=0 and dx^2+2e x+f=0 have a common root, then show that d/p ,e/q ,f/r are in A.P.

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If the equation x^2+px+q=0andx^2+p'x+q'=0 have a common root , prove t...

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If x is real, show that the expression (4x^2+36 x+9)/(12 x^2+8x+1) can...

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  18. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

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  19. If f(x)=(ax^2+x-2)/(a+x-2x^2) has the range R when x in R then

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  20. Let f(x)=(mx^2+3x+4)/(x^(2)+3x+4) , m in R . If f(x) lt 5 for all x i...

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