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If the roots of the equation x^2+x+a=0 b...

If the roots of the equation `x^2+x+a=0` be real and unequal, then prove that the roots of the equation `2x^2-4(1+a)x+2a^2+3=0` are imaginary (a is real).

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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. Find the condition that the roots of the quadratic equation x^2+px+q=0...

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  2. Find the condition that the roots of the quadratic equation x^2+px+q=0...

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  3. If the roots of the equation x^2+x+a=0 be real and unequal, then prove...

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  4. Prove that, if the roots of the equation (a^2+b^2)x^2+2(bc+ad)x+(c^2+d...

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  5. Show that the roots of the equation (a^4+b^4)x^2+4abcdx+(c^4+d^4)=0 ca...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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