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If the equations `a x^2+b x+c=0 and x^3+3x^2+3x+2=0` have two common roots, then a. `a=b=c` b. `a=b!=c` c. `a=-b=c` d. none of these.

A

`a = b ne c`

B

`a = -b = c`

C

`a = b = c`

D

none of these

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. The roots alpha, beta and gamma of an equation x^(3) - 3 a x^(2) + 3 b...

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  2. If b and c are odd integers, then the equation x^2 + bx + c = 0 has-

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  3. 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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  4. If both the roots of the equation ax^(2) + bx + c = 0 are zero, then

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  5. If alpha, beta , gamma, delta are the roots of the equation x^4+x^2+1=...

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  6. The number of real roots of (x+1/x)^3+x+1/x=0 is

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  7. The roots of the equation (3 - x)^(4) + (2 - x)^(4) = (5 - 2x)^(4) are

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  8. The real roots of the equation |x|^3-3x^2+3|x|-2=0 are

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  9. The number of positive integral roots of x^(4) + x^(3) - 4 x^(2) + x +...

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  10. If x, y, z are real and distinct, then x^(2) + 4 y^(2) + x + 1 = 0, is

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  11. The number of values of a for which equations x^3+a x+1=0 and x^4+a x^...

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  12. For what value of m will the equation (x^2-bx)/(ax-c)=(m-1)/(m+1) hav...

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  13. the values of a for which (a^2-1)x^2+2(a-1)x+2 is positive for all rea...

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  14. If alpha and beta are the roots of the equation x^2+sqrt(alpha)x+beta=...

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  15. If a, b, c are in A.P. and if (b-c)x^(2)++(c-a)x+a-b=0and2(c+a)x^(2)+(...

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  16. If the expression [m x-1+(1//x)] is non-negative for all positive real...

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  17. The set of values of p for which the roots of the equation 3x^(2)+2x+p...

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  18. Let alpha and beta, be the roots of the equation x^2+x+1=0. The equati...

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  19. If p and q are the roots of x^2 + px + q = 0, then find p.

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  20. If p ,q ,r are positive and are in A.P., the roots of quadratic equati...

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