" (viii) "2x^(4)-9x^(3)+5x^(2)+3x-1;2+-sqrt(3)

Find all the other zeroes of the polynomial p(x)= 2x^(4)-9x^(3)+5x^(2)+3x-1 , if two of its four zeroes are (2+ sqrt(3))" and "(2- sqrt(3)) .

Divide 2x^(4)-9x^(3)+5x^(2)+3x-8 by x^(2)-4x+1 and verify the division by algorithm.

Find all zeroes of the polynomial 2x^(4)-9x^(3)+5x^(2)+3x-1 if two of its zeroes are 2+sqrt(3) and 2-sqrt(3)

Evaluate lim_(x to sqrt(3)) (3x^(8) + x^(7) - 11x^(6) - 2x^(5) 9x^(4) - x^(3) + 35x^(2) + 6x + 30)/(x^(5) - 2x^(4) + 4x^(2) - 9x + 6)

Evaluate lim_(x to sqrt(3)) (3x^(8) + x^(7) - 11x^(6) - 2x^(5) - 9x^(4) - x^(3) + 35x^(2) + 6x + 30)/(x^(5) - 2x^(4) + 4x^(2) - 9x + 6)

Evaluate: (i) x^(2)+4x+7 when x=2+sqrt(-3) (ii) 2x^(3)-9x^(2)-10x+13 when x=3+sqrt(-5)

If x=1+sqrt""2+sqrt""3 , then the value of 2x^(4)-8x^(3)-5x^(2)+26x-28 is :

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

Determine the nature of roots of the following quadratic equations: (i) 2x^(2)+5x-4=0 (ii) 9x^(2)-6x+1=0 (iii) 3x^(2)+4x+2=0 (iv) x^(2)+2sqrt2x+1=0 (v) x^(2)+x+1=0 (vi) x^(2)+ax-4=0 (vii) 3x^(2)+7x+(1)/(2)=0 (viii) 3x^(2)-4sqrt3x+4=0 (ix) 2sqrt3x^(2)-5x+sqrt3=0 (x) (x-2a)(x-2b)=4ab

Determine the nature of roots of the following quadratic equations: (i) 2x^(2)+5x-4=0 (ii) 9x^(2)-6x+1=0 (iii) 3x^(2)+4x+2=0 (iv) x^(2)+2sqrt2x+1=0 (v) x^(2)+x+1=0 (vi) x^(2)+ax-4=0 (vii) 3x^(2)+7x+(1)/(2)=0 (viii) 3x^(2)-4sqrt3x+4=0 (ix) 2sqrt3x^(2)-5x+sqrt3=0 (x) (x-2a)(x-2b)=4ab