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If a+b+c=0 and a,b,c are rational. Prove...

If `a+b+c=0` and `a,b,c` are rational. Prove that the roots of the equation
`(b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0` are rational.

A

real and unequal

B

real and equal

C

imaginary

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Chapter Test
  1. The sum of all real roots of the equation |x-2|^(2)+|x-2|-2=0 is

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

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

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

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

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

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

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

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

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  10. If alpha,beta and gamma are the roots of x^3+qx + r = 0 thensumalpha/(...

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  11. If alpha, beta are the roots of the equation ax^2 + bx +c=0 then the v...

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  12. If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...

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  13. The maximum number of real roots of the equation x^(2n) -1 = 0, is

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  14. The integral value of k for which the roots of the equation (x-2)x^(...

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  15. If x^(2//3) -7 x^(1//3) + 10 = 0, then the set of values of x, is

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  16. If x^2+2ax+10-3a gt0 for all x in R then

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  17. If the difference between the corresponding roots of x^(2)+ax+b=0and x...

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  18. Product of real roots of the equation t^2x^2+|x|+9=0 a. is always +ve...

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  19. Find the value of a for which the sum of the squares of the roots of t...

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  20. If x^(2)+ax+10=0and x^(2)+bx-10=0 have common root, then a^(2)-b^(2) i...

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