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If 3x^(2) + 2alphaxy + 2y^(2) + 2ax - 4y...

If `3x^(2) + 2alphaxy + 2y^(2) + 2ax - 4y+1` can be resolved into two linear factors, Prove that '`alpha`' is a root of the equation `x^2 + 4ax + 2a^2 + 6 = 0`

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RESONANCE ENGLISH-EQUATIONS -SELF PRACTICE PROBLEMS:
  1. For what value of k ,(4-k)x^2+(2k+4)x+(8k+1)=0 is a perfect square.

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  2. If (x - a) be a factor common to a(1)x^(2) + b(1)x +c and a2x^2 + b(2...

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  3. If 3x^(2) + 2alphaxy + 2y^(2) + 2ax - 4y+1 can be resolved into two li...

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  4. Let 4x^2 - 4(alpha - 2)x + alpha - 2 = 0 (alpha in R) be a quadratic e...

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  5. If P(x) = ax^(2) + bx + c, and Q(x) = -ax^(2) + dx + c, ax ne 0 then p...

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  6. If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common...

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  7. If ax^2 + 2bx + c = 0 and x^2 + 2b(1)x + c(1) = 0 have a common root a...

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  8. If 2p^3 - 9pq + 27r = 0 then prove that the roots of the equations rx^...

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  9. If a, c gt 0 and ax^2 + 2bx + 3c = 0 does not have any real roots the...

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  10. If f(x) =(x-a) (x-b), then show that f(x) ge (a-b)^(2)/4

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  11. Find the least integral value of 'k' for which the quadratic polynomia...

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  12. Find the range of the expression (x^(2) + 34x - 71)/(x^(2) + 2x -7), i...

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  13. Find the interval in which .'m' lies so that the expression (mx^(2) + ...

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  14. Find the value of b for which difference between maximum and minimum v...

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  15. Find all numbers a for each of which the least value of the quadratic ...

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  16. Let x^2-2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then ...

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  17. Find the values of p for which both the roots of the equation 4x^2 - 2...

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  18. Find all values of p so that 6 lies between roots of the equation x^(2...

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  19. Let x^2 - 2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then...

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  20. Find the values of a, for which the quadratic expression ax^2 + (a - 2...

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