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write the degree of the polynomial p^(2)...

write the degree of the polynomial `p^(2)q^(3)+p^(3)q^(2)-p^(3)q^(3)`.

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Degree=6
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(P ^ (2) - (3) / (2) q (2)) ^ (3)

If one root is square of the other root of the equation x^(2)+px+q=0, then the relation between p and q is p^(3)-q(3p-1)+q^(2)=0p^(3)-q(3p+1)+q^(2)=0p^(3)+q(3p-1)+q^(2)=0p^(3)+q(3p+1)+q^(2)=0

Knowledge Check

  • Factorise : p^(3)(q-r)^(3)+q^(3)(r-p)^(3)+r^(3)(p-q)^(3)

    A
    `2pq(p+q)(q+r)(r-p)`
    B
    `3pqr(p-q)(r-q)(r-p)`
    C
    `2pqr(p-q)(q-r)(p-r)`
    D
    `3pqr(p-q)(q-r)(r-p)`

  • If the lines p_(1)x+q_(1)y=1, p_(2)x+q_(2)y=1 and p_(3)x+q_(3)y=1 be concurrent, then the points (p_(1), q_(1)), (p_(2), q_(2)) and (p_(3), q_(3))

    A
    are collinear
    B
    form an equilateral triangle
    C
    form a scalene triangle
    D
    form a right angled triangle

  • If pq ( p + q) = 1 then the value of (1)/( p^(3) q^(3)) - p^(3) - q^(3) is equal to

    A
    1
    B
    2
    C
    3
    D
    4

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    Find the each of the following products: (3p^(2) + q^(2)) (2p^(2) - 3q^(2))

    Verify that (p-q) ( p ^(2) + pq + q ^(2)) = p ^(3) - q ^(3)

    ((2)/(3)p+(3)/(5)q)((2)/(3)p+(3)/(5)q)

    Factorize : p^(3)(q-r)^(3)+q^(3)(r-p)^(3)+r^(3)(p-q)^(3)

    If p = -2, q = - 1 and r = 3, find the value of (i) p^(2) + q^(2) - r^(2) (ii) 2p^(2) - q^(2) + 3r^(2) (iii) p - q - r (iv) p^(3) + q^(3) + r^(3) + 3 pqr (v) 3p^(2) q + 5pq^(2) + 2 pqr (vi) p^(4) + q^(4) - r^(4)

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