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Show that the roots of the equation (a^(...

Show that the roots of the equation `(a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0`
are equal if either `b=0` or `a^(3)+b^(3)+c^(3)-3acb=0`

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If the roots of the equation (c^(2)-ab)x^(2)-2(a^(2)-bc)x+b^(2)-ac=0 are equal,prove that either a=0 or a^(3)+b^(3)+c^(3)=3abc

If the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ca)x+(c^(2)-ab)=0 are equal then the condition is (i)a+b+c=0(ii)a^(3)+b^(3)+c^(3)-3abc=0 (iii) a=0 or a^(3)+b^(3)+c^(3)-3abc=0 (iv) b=0 or a^(3)+b^(3)+c^(3)-3abc=0

The condition for the roots of the equation,(c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac)=0 to be equal is:

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MOTION-QUADRATIC EQUATION-EXERCISE -3 (SUBJECTIVE)
  1. If alpha, beta are the roots fo the equation lamda(x^(2)-x)+x+55=0. If...

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  2. If one root of the equation ax^2+bx+c=0 is the square of the other, pr...

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  3. Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)...

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  4. If a x^2+b x+c=0a n db x^2+c x+a=0 have a common root and a, b, and c ...

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  5. lf the quadratic equations x^2+bx+c=0 and bx^2+cx+1=0 have a common r...

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  6. If the quadratic equations x^2+bx+ca=0 & x^2+cx+ab=0 (where a!= 0) ha...

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  7. Solve the equation x^4 + 4x^3 + 5x^2 + 2x-2=0, one root being -1+sqrt...

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  8. If alpha, beta, gamma are the roots of the equation x^3 + px^2 + qx + ...

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  9. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

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  10. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

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  11. Let alpha,beta,gamma are the roots of the cubic x^3-3x^2+1=0 .Find a c...

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  12. Two roots of a biquadratic x^4-18x^3+ kx^2+ 200x-1984=0 have their pro...

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  13. Suppose a cubic polynomial f(x) = x^3 + px^2 + qx + 72 is divisible by...

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  14. If g(x)=x^(3)+px^(2)+qx+r where p,q,r are integers. If g(0) and g(-1)...

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  15. If x be real then find the range of the following rational expressions...

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  16. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

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  17. Find the range of values of a, such that f(x)=(ax^2+2(a+1)x+9a+4)/(x^2...

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  18. The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2)...

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  19. Find all real numbers x such that (x-1/x)^(1/2)+(1-1/x)^(1/2)=x

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  20. The minimum value of ((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^...

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