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Show that the equations `px^2+qx+r=0` and `qx^2+px+r=0` will have a common root if p+q+r=0 or, p=q=r.

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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. Show that the roots of the equation (a^4+b^4)x^2+4abcdx+(c^4+d^4)=0 ca...

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  2. For what values of m the equations 3x^2+4mx+2=0 and 2x^2+3x-2=0 will h...

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  3. Show that the equations px^2+qx+r=0 and qx^2+px+r=0 will have a common...

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  4. If the two equations x^2+ax+b=0 and x^2+bx+a=0 (aneb) have a common ro...

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  5. IF c is real, show that the roots of the quadratic equation cx^2+(c-1)...

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  6. IF alpha is a root of the equation ax^2+bx+c=0 then show that malpha^2...

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  7. If the quadratic equations x^2+ax+b=0 and x^2+bx+a=0(aneb) have a comm...

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  8. If the roots of the equation x^2-px+q=0 be alpha,beta and the roots of...

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  9. If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5...

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  10. If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5...

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  11. IF x is real , find the greatest and the least value of : (x^2+14x+9...

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  12. IF x is real , find the greatest and the least value of : (x^2-2x+2)...

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  13. Show that for all real values of x the value of (x^2-3x+4)/(x^2+3x+4) ...

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  14. If x is real, show that the value of x/(x^2-5x+9) always lie between 1...

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  15. If x is real show that the expressions (x^2+34x-71)/(x^2+2x-7) has no ...

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  16. If x is real show that the expressions ((x-1)(x+3))/((x-2)(x+4)) has n...

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  17. If x is real then the expressions (x^2+2x-11)/(x-3) assumes those valu...

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  18. If x is real , show that the expressions (x^2-ab)/(2x-a-b) has no real...

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  19. If x is real show that the expressions (3x-5)/(x^2-1) has no value bet...

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  20. IF x is real , find the maximum and minimum values of (x^2-x+1)/(x^2+x...

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