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Theory of Equations Model Question Paper

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 40
    5 x 1 = 5
  1. According to the rational root theorem, which number is not possible rational root of 4x7+2x4-10x3-5?

    (a)

    -1

    (b)

    \(\frac { 5 }{ 4 } \)

    (c)

    \(\frac { 4 }{ 5 } \)

    (d)

    5

  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. 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

  4. 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

  5. If the equation ax2+ bx+c=0(a>0) has two roots ∝ and β such that ∝<- 2 and β > 2, then

    (a)

    b2-4ac=0

    (b)

    b2 - 4ac <0

    (c)

    b2 - 4ac >0

    (d)

    b2 - 4ac≥0

  6. 2 x 2 = 4
  7. 1) \(x+\frac { 1 }{ x } =2\)
    2) ax2+bx+c=0
    3) \(\sqrt { x } +\frac { 1 }{ \sqrt { x } } =4\)
    4) \({ ax }^{ 2 }+\frac { b }{ x } +c=0\)

  8. Ifax + by = 1, Cx2 + dy2 = 1 have only one solution, then
    (1) \(\frac { { a }^{ 2 } }{ c } +\frac { { b }^{ 2 } }{ d } =1\)
    (2) \(x=\frac { a }{ c } \)
    (3) \(x=\frac { c }{ a } \)
    (4) \(x=\frac { b }{ d } \)

  9. 2 x 2 = 4
  10. Find a polynomial equation of minimum degree with rational coefficients, having 2-\(\sqrt{3}\)i as a root.

  11. Show that the equation 2x2−6x+7=0 cannot be satisfied by any real values of x.

  12. 4 x 3 = 12
  13. Find the sum of squares of roots of the equation 2x4-8x+6x2-3=0.

  14. Find the sum of the squares of the roots of ax4+bx3+cx2+dx+e = 0.

  15. If α, β and γ are the roots of the cubic equation x3+2x2+3x+4=0, form a cubic equation whose roots are
    \(\frac { 1 }{ \alpha } ,\frac { 1 }{ \beta } ,\frac { 1 }{ \gamma } \)

  16. Find the number of positive integral solutions of (pairs of positive integers satisfying) x2 - y2 =353702.

  17. 3 x 5 = 15
  18. If 2+i and 3-\(\sqrt{2}\) are roots of the equation x6-13x5+62x4-126x3+65x2+127x-140=0, find all roots.

  19. Solve the equation (x-2)(x-7)(x-3)(x+2)+19=0

  20. If the sum of the roots of the quadratic equation ax2+ bx + c = 0 (abe≠ 0)  is equal to the sum of the squares of their reciprocals, then \(\frac { a }{ c } ,\frac { b }{ a } ,\frac { c }{ b } \)  are H.P.

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