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If a, b, c are positive real numbers, th...

If a, b, c are positive real numbers, then the roots of the equation `ax^(2) + bx + c = 0`

A

are real and are in ratio b : ac

B

are real

C

are imaginary and are in ratio `1 : omega`, where `omega` is a complex cube root of unity

D

are imaginary and are in ratio `-1 : omega`

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Chapter Test
  1. If the roots of a1x^2 + b1x+ c1 = 0 are alpha1 ,beta 1 and those o...

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  2. If the roots of the equation ax^(2)-4x+a^(2)=0 are imaginery and the s...

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  3. If a, b, c are positive real numbers, then the roots of the equation a...

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  4. If the absolute value of the difference of the roots of the equation x...

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  5. If alpha, beta be roots of the equation 375x ^(2) -25x-2=0 and s (n) =...

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  6. The quadratic equation x^(2) + (a^(2) - 2) x - 2a^(2) and x^(2) - 3x +...

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  7. The roots of ax^(2) +bx +c =0 " whose " a ne 0, b ,c in R , " are non...

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  8. The value of m for which the equation x^3-mx^2+3x-2=0 has two roots ...

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  9. If the equation formed by decreasing each root of the a x^2+b x+c=0 by...

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  10. If the roots of the equation ax^2-bx-c=0 are changed by same quantity ...

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  11. If x^2-2rprx+r=0; r=1, 2,3 are three quadratic equations of which each...

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  12. If x ^(2) + px +1 is a factor of ax ^(3) + bx +c, then:

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  13. If (x-1)^3 is a factor of x^4+ax^3+bx^2+cx-1=0 then the other factor ...

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  14. If alpha is a root of the equation x^2+2x-1=0, then prove that 4alpha^...

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  15. If one root of the quadratic equation (a-b)x^2+ax+1=0 is double the ot...

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  16. If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a co...

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  17. If the equation x^(3) + ax^(2) + b = 0, b ne 0 has a root of order 2, ...

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  18. If the roots of the equation x^(2) - bx + c = 0 are two consecutive in...

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  19. If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roo...

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  20. Let S denote the set of all real values of a for which the roots of th...

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