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Prove that the roots of ax^2+2bx+c=0 wi...

Prove that the roots of `ax^2+2bx+c=0`
will be real and distinct if and only if the roots of (a+c) `(ax^2+2bx+c)`=2`(ac-b^2) (x^2+1)` are imaginary

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PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. If alpha and Beta are roots of ax^2+bx+c=0,find the value of (aalpha+b...

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  2. Prove that both the roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-a)...

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  3. Prove that the roots of ax^2+2bx+c=0 will be real and distinct if and...

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  4. Find all roots of equation x^4+2x^3-16x^2-22x+7=0 if one root is 2+sqr...

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  5. Solve for x:4^x+9^x=2(6^x)

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  6. Solve for x: log(a)x+log(x)a=2

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  7. Solve x^(-2)+2x^(-1)-3=0

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  8. 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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  9. If f(x) is a quadratic expression such that f(x)gt0 forall x in R, if ...

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  10. If (cgt 0) and 2ax^2+3bx+5c=0 does not have any real roots, then prove...

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  11. If 2x^3 + ax^2+bx+4 =0 (a and b are positive real numbers) has 3 real ...

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  12. If P(x) = ax^2+bx+c, and Q(x) = -ax^2+dx+c, acne 0, then prove that P(...

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

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

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

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

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

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

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

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