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Algebra || 07.06.2021

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Question 1

If a + b = 1 and a3+b3+3ab = k; then the value of k is

Question 2

If   ;  and  ; then the value of (6a2−35ab+6b2) is:

Question 3

Let α, β be the roots of ax2 + bx + c = 0; γ, δ be the roots of px2 +qx + r = 0; & D1, D2be the respective discriminants of these equations. If α, β, γ, δ are in A.P. Then find the value of D1 : D2

Question 4

If x + x-1 = 2; then the value of (x3 + x-5) is equal to

Question 5

If a³ + 3a² + 9a = 1, then what is the value of  a³ + (3/a) ?

Question 6

If x2 + 2 = 2x, then the value of x4 - x3 + x2 + 2 is:

Question 7

If a and b are roots of the equation ax2 + bx + c = 0, then which equation will have roots (ab + a + b) and (ab − a − b)?

Question 8

If x +  = 4, then find the value of x4 + .

Question 9

Find the value of

Question 10

What are the roots of the quadratic equation 4x2+6x−18 = 0?
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