P(x)=(x+1)(x-2),x=1,2

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)/(sqrt(3)),(2)/(sqrt(3)) (viii) p(x)=2x+1,x=(1)/(2)

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

Assertion (A) : The zeroes of the polynomial p(x)=(x-1)(x-2)(x-3) are 1,2 and 3 Reason (R):The zeroes of a polynomial are the x-coordinates of the points where the graph of polynomial intersects or touches x-axis or the points on the graph where p(x)=0

Verify whether the values of x given in each case are the zeroes of the polynomial or not ? (i) p (x) = 2 x + 1,x =- 1/2 (ii) p (x) = 5x -pi , x = (-3)/(2) (iii) p (x) = x ^(2) -1 , x = pm 1 (iv) p (x) = (x-1) (x +2) , x =-1,-2 (v) p (y) = y ^(2) , y =0 (vi ) p (x) = ax + b, x =- (b)/(a) (vii) f (x) = 3x ^(2) -1 , x =- (1)/(sqrt3) , (2)/(sqrt3) (viii) f (x) =2x -1 , x = (1)/(2), (-1)/(2)

Verify whether the values of x given in each case are the zeroes of the polynomial or not ? (i) p (x) = 2 x + 1,x =- 1/2 (ii) p (x) = 5x -pi , x = (-3)/(2) (iii) p (x) = x ^(2) -1 , x = pm 1 (iv) p (x) = (x-1) (x +2) , x =-1,k-2 (v) p (y) = y ^(2) , y =0 (vi ) p (x) = ax + b, x =- (b)/(a) (vii) f (x) = 3x ^(2) -1 , x =- (1)/(sqrt3) , (2)/(sqrt3) (viii) f (x) =2x -1 , x = (1)/(2), (-1)/(2)

Verify whether the values of x given in each case are the zeroes of the polynomial or not ? (i) p (x) = 2 x + 1,x =- 1/2 (ii) p (x) = 5x -pi , x = (-3)/(2) (iii) p (x) = x ^(2) -1 , x = pm 1 (iv) p (x) = (x-1) (x +2) , x =-1,k-2 (v) p (y) = y ^(2) , y =0 (vi ) p (x) = ax + b, x =- (b)/(a) (vii) f (x) = 3x ^(2) -1 , x =- (1)/(sqrt3) , (2)/(sqrt3) (viii) f (x) =2x -1 , x = (1)/(2), (-1)/(2)

Let P(x)=|(x+1,2,3),(1,x+2,3),(1,2,x+3)| the product of zeros of P(x) is

(d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) (x-1) ^(-2) implies (p,q)=