Slip Test Unit 3 (A2)

12th Standard EM

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MATHEMATICS

HARDWORK NEVER FAILS...
Time : 00:45:00 Hrs
Total Marks : 30

    PART-A

    9 x 2 = 18
  1. Find the sum of squares of roots of the equation 2x4-8x+6x2-3=0.

  2. If α, β, γ  and \(\delta\) are the roots of the polynomial equation 2x4+5x3−7x2+8=0 , find a quadratic equation with integer coefficients whose roots are α + β + γ + \(\delta\) and αβ૪\(\delta\).

  3. Find a polynomial equation of minimum degree with rational coefficients, having \(\sqrt{5}\)\(\sqrt{3}\) as a root.

  4. Solve: (2x-1)(x+3)(x-2)(2x+3)+20=0

  5. Solve the equation 3x3-26x2+52x-24=0 if its roots form a geometric progression.

  6. Determine k and solve the equation 2x3-6x2+3x+k=0 if one of its roots is twice the sum of the other two roots.

  7. Solve the equation : x4-14x2+45 =0

  8. Solve the cubic equations:
    8x3-2x2-7x+3=0

  9. If sin ∝, cos ∝ are the roots of the equation ax2 + bx + c-0 (c ≠ 0), then prove that (n + c)2 - b2 + c2

  10. PART-B

    4 x 3 = 12
  11. Find the condition that the roots of x3+ax2+bx+c = 0 are in the ratio p:q:r.

  12. If p is real, discuss the nature of the roots of the equation 4x2+4px+p+2=0 in terms of p.

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

  14. Find the condition that the roots of ax3+bx2+cx+d=0 are in geometric progression. Assume a,b,c,d ≠0.

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