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If alpha and beta be the roots of the eq...

If `alpha` and `beta` be the roots of the equation `5x^2+bx+c=0` Show that `5x^2+bx+c=5(x-alpha)(x-beta)`
Show also that for all real values of x the expression `5x^2+bx+c` cannot be negative if `alpha` and `beta` are conjugate complex.

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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. IF alpha is a root of the equation ax^2+bx+c=0 then show that malpha^2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. If x be real , find the greatest value of (x+2)/(2x^2+3x+6) .

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  17. If x is real , show that each of the following expressions is capable ...

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  18. If x is real , show that each of the following expressions is capable ...

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  19. If x is real , show that each of the following expressions is capable ...

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  20. IF 3x^2+2(p+q+r)x+pq+qr+rp be a perfect square , prove that p=q=r.

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