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

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

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

If b^(2)gt4ac then roots of equation ax^(4)+bx^(2)+c=0 are all real & distinct if :

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 R

Prove that the equation x^(4)-4x -1 =0 has two different real roots .

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

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

If a+b+c=0(a,b, c are real), then prove that equation (b-x)^2-4(a-x)(c-x)=0 has real roots and the roots will not be equal unless a=b=c .

If a+b+c=0(a,b, c are real), then prove that equation (b-x)^2-4(a-x)(c-x)=0 has real roots and the roots will not be equal unless a=b=c .