Which of the following equations has the sum of its roots as 3? (a) `x^2+3x-5=0` (b) `-x^2+3x+3=0` (c) `sqrt2x^2-3/sqrt2 x-1=0` (d) `3x^2-3x-3=0`

Which of the following equations has the sum of its roots as 3? (a) x^2+3x-5=0 (b) -x^2+3x+3=0 (c) sqrt(2)x^2-3/(sqrt(2))x-1=0 (d) 3x^2-3x-3=0

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) 2x^2-3x+5=0 (ii) 3x^2-4sqrt(3)x+4=0 (iii) 2x^2-6x+3=0

Which of the following are quadratic equations? x^2+2sqrt(x)-3=0 (ii) 3x^2-4x+2=0 (iii) 2x^2-2x+4

Find the roots of the following quadratic equations by factorisation : (i) x^(2)-3x-10=0 (ii) 2x^(2)+x-6=0 (iii) sqrt2x^(2)+7x+5sqrt2=0 (iv) 2x^(2)-x+(1)/(8)=0 (v) 100x^(2)-20x+1=0 (vi) 2x^(2)+az-a^(2)=0

Which of the following are quadratic equations? (i) x-3/x=x^2 (ii) 2x^2-sqrt(3)x+9=0 (iii) x^2-2x-sqrt(x)-5=0

Solve the following quadratic equations : (i) 9x^(2) - 8x+2=0 (ii) sqrt7 x^(2) +x+ sqrt7=0 (iii) 2sqrt3x^(2) -sqrt2 x + 3sqrt3 =0

Which of the following are quadratic equations? 3x^2-5x+9=x^2-7x+3 (ii) x+1/x=1 (iii) x^2-3x=0

Solve the following equations where x in R a) (x-1)|x^(2)-4x+3|+2x^(2)+3x-5=0 b) |x^(2)+4x+3|+2x+=0 c) |x+3|(x+1)+|2x+5|=0

If the represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , on in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is (1) y^2-x^2+2sqrt(3)x+3=0 (2) y^2-x^2+2sqrt(3)x-3=0 (3) y^2-x^2-2sqrt(3)x+3=0 (4) y^2-x^2+3=0

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+4sqrt3x+3=0 (iv) 2x^2+x+4 = 0