Determine the nature of the roots of the following quadratic equations: `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`

Determine the nature of the roots of the following quadratic equation 2(a^(2)+b^(2))x^(2)+2(a+b)x=1=0

Find the roots of the quadratic equation a^(2)b^(2)x^(2)+b^(2)x-a^(2)x-1=0

Find the roots of the quadratic equation: a^(2)b^(2)x^(2)+b^(2)x-a^(2)x-1=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 quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

Show that the roots of the quadratic equation: (b - c)x^(2) + (c - a) x + (a - b) = 0 are equal if c + a = 2b.

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

In the quadratic equation 4x^(2) - 2 ( a + c - 1) x + ac - b = 0 (a gt b gt c)

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