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If alpha,beta be the roots x^2+px-q=0 an...

If `alpha,beta` be the roots `x^2+px-q=0` and `gamma,delta` be the roots of `x^2+px+r=0, p+rphi0`,then `((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))` is equal to

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If alpha,beta are the roots x^2+px+q =0 and gamma,delta are the roots of x^2+rx+s =0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p,q,r and s. Deduce the condition that the equation may have a common root.

IF alpha,beta and gamma,delta be the roots of the equation x^2+px-r=0 and x^2+px+r=0 respectively, prove that (alpha-gamma)(alpha-delta)=(beta-gamma)(beta-delta)

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Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the roots of x^2-4x+q=0 . If alpha,beta,gamma are in GP , then the integer values of p and q respectively are:

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Let alpha,beta be the roots of the equation x^2-4x+A=0 and gamma,delta be the roots of the equation x^2-36x+B=0 . If alpha,beta,gamma and delta are In G.P. having positive common ratio, find the value of A and B.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  3. If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of ...

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

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

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

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

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

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

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

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

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  17. For alt=0 , determine all real roots of the equation x^2-2a|x-a|-3a^2=...

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  18. Solve for x :(5+2sqrt(6))^(x^2-3)+(5-2sqrt(6))^(x^2-3)=10.

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  19. If one root of the quadratic equation ax^2+bx+c=0 is equal to the n^th...

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  20. If a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a com...

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