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If alpha and beta are roots of the equat...

If `alpha and beta` are roots of the equation `a x^2+b x+c=0,` then the roots of the equation `a(2x+1)^2+b(2x+1)(x-3)+c(x-3)^2=0` are a. `(2alpha+1)/(alpha-3),(2beta+1)/(beta-3)` b. `(3alpha+1)/(alpha-2),(3beta+1)/(beta-2)` c. `(2alpha-1)/(alpha-2),(2beta+1)/(beta-2)` d. none of these

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are rea...

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  3. If alpha and beta are roots of the equation a x^2+b x+c=0, then the ro...

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  4. If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx...

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  5. Graph of y = f(x) is as shown in the following figure. Find th...

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  6. In how many points graph of y=x^3-3x^2+5x-3 intersect the x-axis?

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  7. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

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  8. If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find it...

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  9. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

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  10. Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5...

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

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

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  14. Which of the following pair of graphs intersect? y=x^2-xa and y=1 y...

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  15. If alphaa n dbeta are the rootsof he equations x^2-a x+b=0a n dAn=alp...

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  16. If alpha,beta are the roots of x^2+p x+q=0 and gamma,delta are the roo...

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

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  19. Let p(x)=0 be a polynomial equation of the least possible degree, with...

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  20. The number of values of a for which equations x^3+a x+1=0 and x^4+a x^...

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