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Theorem : Let a, b, c in R and a ne0. Th...

Theorem : Let a, b, c `in` R and a `ne`0. Then the roots of `ax^(2)+bx+c=0` are non-real complex numbers if and only if `ax^(2)+bx+c` and a have the same sign for all ` x in R`.

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The correct Answer is:
Hence `4ac - b^(2) gt 0,` so that `b^(2)-4ac lt 0` Thus `b^(2)-4ac lt 0` if and only if `ax^(2)+bx+c` and a have the same sign for all real x.
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-QUADRATIC EXPRESSIONS-TEXTUAL EXERCISES
  1. Theorem : Let a, b, c in R and a ne0. Then the roots of ax^(2)+bx+c=0 ...

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  2. Find the roots of the following equations. x^(2)-7x+12=0

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  3. Find the roots of the following equations. -x^(2)+x+2=0

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  4. Find the roots of the following equations. 2x^(2)+3x+2=0

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  5. Find the roots of the following equations. sqrt(3)x^(2)+10x-8sqrt(3)...

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  6. Find the roots of the following equations. 6sqrt(5)x^(2)-9x-3sqrt(5)...

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  7. Form quadratic equation whose roots are : 2,5

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  8. Form quadratic equation whose roots are : (m)/(n), (n)/(m) (m ne 0, ...

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  9. Form quadratic equation whose roots are : (p-q)/(p+q), (-p+q)/(p-q),...

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  10. Form quadratic equation whose root 7 pm 2sqrt(5)

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  11. Form quadratic equation whose roots are : -3 pm 5i

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  12. Find the nature of the roots of the following equation, without findin...

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  13. Find the nature of the roots of the following equation, without findin...

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  14. Find the nature of the roots of the following equation, without findin...

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  15. Find the nature of the roots of the following equation, without findin...

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  16. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

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  17. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

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  18. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

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  19. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

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  20. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

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  21. Find the values of m for which the following equations have equal root...

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