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If x in R ,a n da ,b ,c are in ascendin...

If `x in R ,a n da ,b ,c` are in ascending or descending order of magnitude, show that `(x-a)(x-c)//(x-b)(w h e r ex!=b)` can assume any real value.

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. If x=1 and x=2 are solutions of equations x^3+a x^2+b x+c=0 and a+b=1,...

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

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  4. Prove that graphs y=2x-3 and y=x^2-x never intersect.

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  5. Which of the following pair of graphs intersect ? (i) y = x^(2) - x ...

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  6. If alpha and beta are the rootsof he equations x^2-a x+b=0a n dAn=alph...

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  7. If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of ...

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  8. If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roo...

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  9. The value m for which one of the roots of x^2-3x+2m=0 is double of one...

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  10. LetP(x)=0 be the polynomial equation of least possible degree with rat...

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  11. The value of 'a' for which the equation x^3+ax+1=0 and x^4+ax^2+1=0, w...

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  12. If (mr ,1/mr) where r=1,2,3,4, are four pairs of values of x and y ...

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  13. If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^2+...

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  14. If tantheta1,tantheta2,tantheta3 are the real roots of the x^3-(a+1)x...

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  15. If roots of an equation x^n-1=0a r e1,a1,a2,..... a(n-1), then the v...

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  16. If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,be...

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  17. Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if...

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  18. Let S be a square of unit area. Consider any quadrilateral which has o...

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  19. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

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  20. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

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