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Let P(x)equiv ((x-a)(x-b))/((c-a)(c-b))....

Let P(x)`equiv ((x-a)(x-b))/((c-a)(c-b)).c^2+((x-b)(x-c))/((a-b)(a-c)).a^2+((x-c)(x-a))/((b-c)(b-a)).b^2`
Prove that P(x) has the properly that P(y) =`y^2` for all y`in`R.

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PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. If alpha,beta are the roots x^2+px+q=0 and gamma,delta are the roots o...

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  2. Find condition if ax^3+bx^2+cx+d=0, has exactly one real root, (a,b,c,...

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  3. Let P(x)equiv ((x-a)(x-b))/((c-a)(c-b)).c^2+((x-b)(x-c))/((a-b)(a-c))....

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  4. Solve the equation (x^2-6x)^2=81+2(x-3)^2

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  5. Show f(x)=x^3+px+q=0 has a repeated root if 4p^3+27q^2=0

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  6. Show x^5-2x^2+7=0 has atleast two imaginary roots.

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  7. Solution set of x satisfying abs(x/(x-1))+absx=x^2/abs(x-1) is

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  8. Solve the equation abs(x-abs(4-x))-2x=4

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  9. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  10. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  11. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  12. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

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  13. Find two negative integers whose difference is 3 and sum of their squa...

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  14. If alpha and beta are roots of ax^2+bx+c=0 then prove that (alpha/bet...

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  15. If (p^2+2)x^2+2p^2x+(P^2-4)=0 has root of opposite sign,then find the ...

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  16. Find the condition such that the quadratic equations ax^2+bx+c=0 and x...

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  17. If (x-1) is the factors fo polynomial x^3-px+q, then prove that p-q=1

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  18. Two roots of the equation,x^3+qx^2+11x-p=0 are 2 and 3, find (p-q)

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  19. Find the values of K for which the inequality (x-3k)(x-k-3)lt0 is sati...

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  20. Let alpha and beta be the roots of the equation ax^2+2bx+c=0 and alpha...

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