" (i) "2^(2x)-2^(x+3)+2^(4)=0quad " (ii) "3^(2x+4)+1=2*3^(x+2)

Solve the following equations for x\ : (i)\ 2^(2x)-\ 2^(x+3)+2^4=0 (ii)\ 3^(2x+4)+1=2. 3^(x+2)

(ii) (2x + 1/2)(3x/2−1/4)

Examine the nature of the roots of the equations (i) 2x^(2)+2x+3=0 (ii) 2x^(2)-7x+3=0 (iii) x^(2)_5x-2=0 (iv) 4x^(2)-4x+1=0

4 (2x-3) ^ (2) - (2x-3) -14 = 0

factorise (i) 2x^(3)-3x^(2)-17x+30 (ii) x^(3) -6x^(2)+11x-6 (iii) x^(3)+x^(2)-4x-4 (iv) 3x^(2)-x^(2)-3x+1

Find the roots of the quadratic equations by applying the quadratic formula.(i) 2x^(2)-7x+3=0 (ii) 2x^(2)+x-4=0 (iii) 4x^(2)+4sqrt(3)x+3=0( iv )2x^(2)+x+4=0

Solve for x (i) 2^(|x+1|)+2^(|x|)=6 and x in I (ii) x^(2)+x+1+|x-3| le |x^(2)+2x-2| (iii) |2x-4|-2|x^(2)+x-3|+2|x-1||x+1|=0

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4