9a^(2)b^(2)x^(2)-48abcdx+64c^(2)d^(2)=0

Determine the nature of the roots for the following quadratic equations 9a^(2)b^(2)x^(2)-24abcdx+16c^(2)d^(2)=0, ane0 , bne0

Determine the nature of the roots of the following quadratic equations: 9a^(2)b^(2)x^(2)-24abcdx+16c^(2)d^(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

Prove that the roots of the equation (a^(4)+b^(4))x^(2)+4abcdx+(c^(4)+d^(4))=0 cannot be different,if real.

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

If (a)/(b)=(c)/(d) then (a+b)/(a-b)=(c+d)/(c-d),ab=cd ,(a^(2)+b^(2))/(a^(2)-b^(2))=(c^(2)+d^(2))/(c^(2)-d^(2)), ad-dc=0

If the roots of (a^(2)+b^(2)) x^(2)+2(a c+b d) x+(c^(2)+d^(2))=0 are equal then

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 and c are positive real number and ellipse (x^(2))/(4c^(2))+(y^(2))/(c^(2))=1 has four distinct points in comman with the circle x^(2)+y^(2)=9a^(2), then (A) 6ac+9a^(2)-2c^(2)>0(B)6ac+9a^(2)-2c^(2) 0(D)6ac-9a^(2)-2c^(2)<0

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)