Determine the nature of the roots of the following quadratic equations:
(i)`9a^2b^2x^2-24 a b c dx+16 c^2d^2=0,\ \ a!=0,\ b!=0`
(ii)`2(a^2+b^2)x^2+2(a+b)x+1=0`
(iii) `(b+c)x^2-(a+b+c)x+a=0`

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

If the roots of the equation (a^2+b^2)x^2-2(a c+b d)x+(c^2+d^2)=0 are equal, prove that a/b=c/d

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

Without determining the roots of the following equations comment their nature: (i) 6sqrt3x^(2)-4x+sqrt3=0 (ii) 9a^(2)b^(2)x^(2)-48abcdx+64c^(2)d^(2)=0 (iii) a^(2)x^(2)+2abx=b^(2),a^(2)ne0 (iv) 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 (v) (b+c)x^(2)-(a+b+c)x+a=0

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

Using quadratic formula, solve the following equation for x: a b x^2+(b^2-a c)x-b c=0

If sectheta+ tantheta = 1 , then root of the equation (a-2b + c)x^2 +(b-2c+ a)x+(c-2a+b) = 0 is:

If the equation (a^2+b^2)x^2-2(a c+b d)x+c^2+d^2=0 has equal roots, then (a) a b=c d (b) a d=b c (c) a d=sqrt(b c) (d) a b=sqrt(c d)

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are