`|{:(" "1," "1," "x),(p+3,p+1,p+x),(" "3,x+1,x+1):}|=0`

1.Solve for x: abs ((1,1,x),(p+1,p+1,p+x),(3,x+1,x+2)) =0

If p ne 0 , then the solutions of the equation |(1,1,x),(p+1,p+1,p+x),(3, x+1,x+2)|=0 are -

1,1,xp+3,p+1,p+x3,x+1,x+1]|=0

Solve the following: |[1, 1,x], [p+1,p+1,p+x],[3,x+1,x+2]|=0

IF 25025 = p_(2)^(x1),p_(2)^(x2),p_(3)^(x3),p_(4)^(x4) find the values of p_(1), pz, p_(3), p_(4) and x_(1), x_(2), x_(3), x_(4) .

If each pair of the three equations x^(2) - p_(1)x + q_(1) =0, x^(2) -p_(2)c + q_(2)=0, x^(2)-p_(3)x + q_(3)=0 have common root, prove that, p_(1)^(2)+ p_(2)^(2) + p_(3)^(2) + 4(q_(1)+q_(2)+q_(3)) =2(p_(2)p_(3) + p_(3)p_(1) + p_(1)p_(2))

Let p(x) be a function defined on R such that p '(x)""=""p '(1""""x) , for all x in [0,""1],""p(0)""=""1 and p(1)""=""41 . Then int_0^1p(x)dx equals (1) 21 (2) 41 (3) 42 (4) sqrt(41)

If p_(1)^(x_(1))timesp_(2)^(x_(2))timesp_(3)^(x_(3))timesp_(4)^(x_(4))=11340 where p_(1), p_(2), p_(3), p_(4) are primes in ascending order and x_(1), x_(2), x_(3), x_(4) are integers, find the value of p_(1), p_(2), p_(3), p_(4) and x_(1), x_(2), x_(3), x_(4) .

Verify whether the following are zeroes of the polynomial, indicated against them . (i) p(x)=3x+1, x=-1/3 (ii) p(x) = 5x-pi,x=4/5 (iii) p(x) = x^2-1,x=1,-1 (iv) p(x) = (x+1) (x-2) , x = -1,2 (v) p(x) =x^2,x=0 (vi) p(x) =lx+m,x=-m/l (vii) p(x)=3x^2-1,x=-1/sqrt3,2/sqrt3 (viii) p(x) = 2x+1,x=1/2