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`

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

Roots of the following equation are 6x^2 + 4x - 2 = 0

Write the discriminant of the following quadratic equations and mention the nature of the root : (a) 9x^(2)-6x+1=0 (b) x^(2)+x-12=0 (c ) 4sqrt3x^(2)+5x+2sqrt3=0

Which of the following are quadratic equations? x^(2)-6x+4=0( ii) 2x^(2)-7x=0

Find the discriminant of each of the following equations: (i) 2x^(2)-7x+6=0" "(ii)" "3x^(2)-2x+8=0 (iii) 2x^(2)-5sqrt(2)x+4=0" "(iv)" "sqrt(3)x^(2)+2sqrt(2)x-2sqrt(3)=0 (v) (x-1)(2x-1)=0" "(vi)" "1-x=2x^(2)

Find the nature of roots of the following quadratic equations. If the real roots exist, (i) 2x^(2)-3x+5=0 (ii) 3x^(2)-4sqrt3x+4=0 (iii) 2x^(2)-6x+3=0

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

The largest integral value of k for which the equation (x-1)(x-2)(x-3)(x-4)+k=0 has real roots is a root of the equation (a) x^(2)-3x+2=0 (b) x^(2)+3x+2=0 (c) x^(2)-7x+12=0(d)x^(2)+7x+12=0

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

Solve the following inequalities. (a) |2x-3| lt 1, (b) (x-2)^(2) ge 4 , (c) x^(2) ge 4 , (c) x^(2)+2x-8 le 0 , (d) |x^(2) -7x+12| gt x^(2)-7x+12 .