" (1) "3x^(2)-4x-12=0

3x^(2)-5x-12=0

Which of the following equations has 2 as a root? (a) x^(2)-4x+5=0 , (b) x^(2)+3x-12=0 (c) 2x^(2)-7x+6=0 , (d) 3x^(2)-6x-2=0

Find the nature of the roots of the following quadratic equations: (i) 2x^(2)-8x+5=0" "(ii)" "3x^(2)-2sqrt(6)x+2=0 (iii) 5x^(2)-4x+1=0" "(iv)" "5x(x-2)+6=0 (v) 12x^(2)-4sqrt(15)x+5=0" "(vi)" "x^(2)-x+2=0

Find the equation of the radical axis of circles x^(2)+y^(2)+x-y+2=0 and 3x^(2)+3y^(2)-4x-12=0

The cubic polynomial with leading coefficient unity all whose roots are 3 units less than the roots of the equation x ^(3) -3x ^(2) -4x +12=0 is denoted as f (x) then f '(x) is equal to :

Equation of the tangent to x^(2)-4x-8y+12=0 at (4,(3)/(2)) is

Show that (x-3) is a factor of the polynomial x^(3)-3x^(2)+4x-12

If two roots of x^(3)7x^(2)+4x+12=0 are in the ratio 1:3 then the roots are

The equation of the normal at (1,2) to the circle x^(2)-y^(2)-4x-6y-12=0 is