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If x^2+ax+bc=0 and x^2+bx+ac=0 have a co...

If `x^2+ax+bc`=0 and `x^2+bx+ac`=0 have a common root, show their other root satisfies the equation `x^2+cx+ab`=0

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PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. Find the common root of x^2-3x+2=0 and x^2+x-2=0

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  2. Find the condition if equations ax^2+bx+c=0 and x^2+2x+3=0 have a comm...

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  3. If x^2+ax+bc=0 and x^2+bx+ac=0 have a common root, show their other ro...

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  4. If alpha,beta are the roots x^2+px+q=0 and gamma,delta are the roots o...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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