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

A

`a^(2) + c^(2) = -ab`

B

`a^(2) - c^(2) = -ab`

C

`a^(2) - c^(2) = ab`

D

none of these

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

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

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

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

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

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

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

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

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

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  12. The sum of all real roots of the equation |x-2|^(2)+|x-2|-2=0 is

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  13. The twice of the product of real roots of the equation (2x+3)^(2)- 3|...

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  14. If a+b+c=0 and a,b,c are rational. Prove that the roots of the equatio...

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  15. If secalpha, tan alpha, " are roots of " ax^(2) + bx +c =0 , then

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  16. If the roots of the equation x^(3) + bx^(2) + 3x - 1 = 0 form a non-de...

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  17. Let [x] denote the greatest integer less than or equal to x. Then, int...

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  18. the number of non-zero solutions of the equation x^2-5x-(sgn x)6=0 is.

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  19. Find the value of a for which one root of the quadratic equation (a^2-...

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  20. If alpha, beta, gamma are the roots of the equation x^(3) + ax^(2) + b...

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