(ii)` (2x+1)(3x-2)=6(x+1)(x-2)`

write the coefficient of x^(2) in each of the following (i) (pi)/(6)x+x^(2)-1 (ii) 3x-5 (iii) (x-1)(3x-4) (iv) (2x-5)(2x^(2)-3x+1)

Solve for x : (1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)

Which of the following are quadratic equations in x? (i)" "x^(2)-x+3=0" "(ii)" "2x^(2)+(5)/(2)x-sqrt(3)=0 (iii)" "sqrt(2)x^(2)+7x+5sqrt(2)=0" "(iv)" "(1)/(3)x^(2)+(1)/(5)x-2=0 (v)" "x^(2)-3x-sqrt(x)+4=0" "(vi)x-(6)/(x)=3 (vii)" "x+(2)/(x)=x^(2)" "(viii)" "x^(2)-(1)/(x^(2))=5 (ix)" "(x+2)^(3)=x^(3)-8" "(x)" "(2x+3)(3x+2)=6(x-1)(x-2) (xi) " "(x+(1)/(x))^(2)=2(x+(1)/(x))+3

Evaluate: (i) (x^(2)+3x-1)/((x+1)^(2))dx (ii) int(2x-1)/((x-1)^(2))dx

prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1))|=6x^(2)(1-x^(2))

int (dx)/((x+1)(2x+1)) (ii) int (x-1)/((x-2)(x-3)) dx .

Check whether the following are quadratic equation (i) (x+1)^2=2(x-3) (ii) x^2-2x=(-2)(3-x) (iii) (x-2)(x+1)=(x-1)(x+3) (iv) (x-3)(2x+1)=x(x+5) (v) (2x-1)(x-3)=(x+5)(x-1) (vi) x^2+3x+1=(x-2)^2 (vii) (x+2)^3=2x(x^2-1) (viii) x^3-– 4x^2 – x + 1 = (x – 2)^3

If f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1))|, then f(100) is equal to - (i)0 (ii)1 (iii)100 (iv)-100

Solvef or x,(1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)