`|[1,1,x] , [p+3,p+1,p+x] , [3,x+1,x+1]|=0`

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

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

Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in [0, 1], P(0)=1, P(1) =41 then int_(0)^(1)P(x)dx=

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_0^1 p(x) dx equals :

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) .

For each of the following polynomials, find p(0), p(1) and p(3) : p(x) = (1)/(3)x^(2) + 4x -1

P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p(x) has maxima at x = -1 and p(x) has minima at x=1 then The value of P(1) is