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#### Slip Test Unit 3 (A2)

12th Standard EM

Reg.No. :
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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.