Polynomials - Past Year Questions

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Q1:

If a1,a2,...,a8a_1, a_2, ..., a_8 are the roots of the equation x8+x7+...+x+1=0x^8 + x^7 + ... + x + 1 = 0, then the value of a12025+a22025+...+a82025a_1^{2025} + a_2^{2025} + ... + a_8^{2025} is
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Option 3
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Q2:

If 8x2−2kx+k=08x^2 - 2kx + k = 0 is a quadratic equation in xx, such that one of its roots is pp times the other, and p,kp, k are positive real numbers, then kk equals
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Option 3
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Q3:

Let P(x)P(x) be a quadratic polynomial such that
∣P(0)P(1)P(0)P(2)∣=0\left|\begin{array}{ll} P(0) & P(1) \\ P(0) & P(2) \end{array}\right|=0
Let P(0)=2P(0)=2 and P(1)+P(2)+P(3)=14P(1)+P(2)+P(3)=14. Then P(4)P(4) equals
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Option 3
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Q4:

Let f(x)=a2x2+2bx+cf(x) = a^2x^2 + 2bx + c where, a≠0a \neq 0, b,cb, c are real numbers and xx is a real variable then
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Option 2
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Q5:

The difference between the maximum real root and the minimum real root of the equation (x2−5)4+(x2−7)4=16(x^2 - 5)^4 + (x^2 - 7)^4 = 16 is
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Option 4
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Q6:

The number of real solutions of the equation (x2−15x+55)x2−5x+6=1(x^2 - 15x + 55)^{x^2-5x+6} = 1 is:
6
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Q7:

If the harmonic mean of the roots of the equation (5+2)x2−bx+8+25=0(5 + \sqrt{2}) x ^ 2 - bx + 8 + 2\sqrt{5} = 0 is 44 then the value of bb is
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Option 4
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Polynomials - Past Year Questions (Free PDF Download)

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