[qquad +2m=0" क "],[qquad " (ii) "2x^(2)-x+9=x^(2)+4x+3,quad x=2,quad x=3]

In each of the following, determine whether the given values are solutions of the given equation or not: (i) 2x^2-x+9=x^2+4x+3,\ \ x=2,\ \ x=3 (ii) x^2-sqrt(2)x-4=0,\ \ x=-sqrt(2),\ \ x=-2sqrt(2) (iii) a^2x^2-3a b x+2b^2=0,\ \ x=a//b ,\ \ x=b//a

Find the roots of the following quadratic equations i) 6sqrt5 x^(2) – 9x -3sqrt5 = 0 ii) x^(2) - x - 12 = 0 iii) 2x^(2) - 6x + 7 = 0 iv) 4x^(2) - 4x+17 = 3x^(2) -10x-17 v) x^(2) + 6x + 34 = 0 vi) 3x^(2) + 2x - 5 = 0

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

Solve the following quadratic equations by completing square method : (i) x^(2) + 8x-48=0 (ii) x^(2) - 4x - 3 = 0 (iii) 9 x^(2) - 12 x + 2 = 0 (iv) x^(2) + 8x+ 9 = 0

lim_(x rarr oo) (3x^(3) + 2x^(2) - 7x + 9)/(4x^(3) + 9x -2)

Analyze the roots of the following equations: (i) 2x^(3) - 9x^(2) + 12x - (9//2) = 0 (ii) 2x^(3) - 9x^(2) + 12x - 3 = 0

In each of the following find the value of 'a' : (i) 4x^(2)+ax+9=(2x+3)^(2) (ii) 9x^(2)+(7a-5)x+25=(3x+5)^(2)