Theory of Equations One Mark Questions

12th Standard EM

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Maths

Time : 00:30:00 Hrs
Total Marks : 15
    10 x 1 = 10
  1. If α,β and γ are the roots of x3+px2+qx+r, then \(\Sigma \frac { 1 }{ \alpha } \) is

    (a)

    -\(\frac { q }{ r } \)

    (b)

    \(\frac { p }{ r } \)

    (c)

    \(\frac { q }{ r } \)

    (d)

    -\(\frac { q }{ p } \)

  2. The polynomial x3-kx2+9x has three real zeros if and only if, k satisfies

    (a)

    |k|≤6

    (b)

    k=0

    (c)

    |k|>6

    (d)

    |k|≥6

  3. If x3+12x2+10ax+1999 definitely has a positive zero, if and only if

    (a)

    a≥0

    (b)

    a>0

    (c)

    a<0

    (d)

    a≤0

  4. The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)rxr is

    (a)

    0

    (b)

    n

    (c)

    < n

    (d)

    r

  5. If a, b, c ∈ Q and p +√q (p,q ∈ Q) is an irrational root of ax2+bx+c=0 then the other root is

    (a)

    -p+√q

    (b)

    p-iq

    (c)

    p-√q

    (d)

    -p-√q

  6. The quadratic equation whose roots are ∝ and β is

    (a)

    (x - ∝)(x -β) =0

    (b)

    (x - ∝)(x + β) =0

    (c)

    ∝+β=\(\frac{b}{a}\)

    (d)

    ∝.β=\(\frac{-c}{a}\)

  7. Ifj(x) = 0 has n roots, thenf'(x) = 0 has __________ roots

    (a)

    n

    (b)

    n -1

    (c)

    n+1

    (d)

    (n-r)

  8. If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then

    (a)

    \(\frac{1}{3}\) ≤k≤

    (b)

    k≥5

    (c)

    k≤0

    (d)

    none

  9. Let a > 0, b > 0, c >0. h n both th root of th quatlon ax2+b+C= 0 are

    (a)

    real and negative

    (b)

    real and positive

    (c)

    rational numb rs

    (d)

    none

  10. The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has

    (a)

    no solution

    (b)

    one solution

    (c)

    two solution

    (d)

    more than one solution

  11. 5 x 1 = 5
  12. 6x6 - 35x5 + 56x4 -56x2 + 35x - 6 = 0

  13. (1)

    Reciprocal equation of type I

  14. p(x)=xn.p\(\left( \frac { 1 }{ x } \right) \)

  15. (2)

    4 Change of sign

  16. 2x7-3x6-4x5+5x4+6x3-7x+8 = 0

  17. (3)

    at least 6 imaginary roots

  18. 9x9+2x5-x4-7x2+2=0

  19. (4)

    4 Change of sign

  20. x9-5x8 -14x7=0

  21. (5)

    even degree reciprocal equation of type II

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