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Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C a...

Let `f(x)=A x^2+B x+c ,w h e r eA ,B ,C` are real numbers. Prove that if `f(x)` is an integer whenever `x` is an integer, then the numbers `2A ,A+B ,a n dC` are all integer. Conversely, prove that if the number `2A ,A+B ,a n dC` are all integers, then `f(x)` is an integer whenever `x` is integer.

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PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
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  2. Solve x^(-2)+2x^(-1)-3=0

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  8. If alpha,beta,gaama are the roots of the cubic x^3+qx+r=0, find the eq...

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  11. f(x)=x^2-(m-3)x+m=0 is a quadratic equation, find values of m for whic...

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  14. f(x)=x^2-(m-3)x+m=0 is a quadratic equation, find values of m for whic...

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  15. If,alpha be the root of equation ax^2+bx+c=0 and beta be root of -ax^2...

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  19. For what value of 'm' inR, both roots of the equation x^2-6mx+9m^2-2m+...

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