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IF alpha be a root of the quadratic equa...

IF `alpha` be a root of the quadratic equation `4x^2+2x-1=0`, Let prove that `4alpha^3-3alpha` is the other root.

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If alpha be a root of the quadratic equaiton 4x^2+2x-1=0 .Prove that 4alpha^3-3alpha is the other root.

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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. IF p^3-q(3p-1)+q^2=0 , find the relation between the roots of the equa...

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  2. Let a,b,c be real numbers with ane0 and let alpha,beta be the roots of...

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  3. IF alpha be a root of the quadratic equation 4x^2+2x-1=0, Let prove th...

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  4. Letalpha,beta be the roots of the equation x^2-3x+a=0 and gamma,delta ...

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  5. IF a,b,c are real, show that the roots of each of the following equati...

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  6. IF a,b,c are real, show that the roots of each of the following equati...

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  7. IF a,b, are real, show that the roots of each of the following equatio...

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  8. IF a,b,c are real, show that the roots of each of the following equati...

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  9. If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show...

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

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

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

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

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

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

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

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

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

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

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