" 7."quad x^(2)-2x+(3)/(2)=0

(2x+3)(3x-7)=0

If f(x)=4x^(2)+3x-7 and alpha is a common root of the equation x^(2)-3x+2=0 and x^(2)+2x-3=0 then the value of f(alpha) is

If 3x^(2)-7x+2=0 and 15x^(2)-11x+a=0 have a common root and a is a positive real number then the sum of the roots of the equation 15x^(2) -ax +7=0 is

(2x-3)/(3x-7)>0

(2x ^ (2) + 3y ^ (2) -7) xdx- (3x ^ (2) + 2y ^ (2) -8) is = 0

Without solving, find the nature of the roots of the following equations: (i) 3x^(2)-7x+5=0 . (ii) 4x^(2)+4x+1=0 . (iii) 3x^(2)+7x+2=0 . (iv) x^(2)+px-q^(2)=0 .

Examine the nature of the roots of the equations (i) 2x^(2)+2x+3=0 (ii) 2x^(2)-7x+3=0 (iii) x^(2)_5x-2=0 (iv) 4x^(2)-4x+1=0

Discuss the nature of the following quadratic equations without finding the roots i) x^(2)-12x+32=0 ii) 2x^(2)-7x+10=0 iii) 4x^(2)-20x+25=0 iv) 3x^(2)+7x+2=0