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12th Standard English Medium Maths Subject Theory of Equations Creative 5 Mark Questions with Solution

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. If the sum of the roots of the quadratic equation ax2+ bx + c = 0 (abc ≠ 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.

  2. If a, b, c, d and p are distinct non-zero real numbers such that (a2+b2+c2) p2-2 (ab+bc+cd) p+(b2+c2+d2)≤ 0 then prove that a, b, c, d are in G.P and ad = bc

  3. If c ≠ 0 and \(\frac { p }{ 2x } =\frac { a }{ x+x } +\frac { b }{ x-c } \) has two equal roots, then find p. 

  4. If the equation x2 + bx + ca = 0 and x2 + cx + ab = 0 have a comnion root and b≠c, then prove that their roots will satisfy the equation x2 + ax + bc = 0.

  5. Solve: (2x2 - 3x + 1) (2x2 + 5x + 1) = 9x2.

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