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.

Prove that the roots of the equation (b-c)x^(2)+2(c-a)x+(a-b)=0 Show that the root are always real

Prove that the roots of the quadratic equation ax^(2)-3bx-4a=0 are real and distinct for all real a and b,where a!=b.

-If a,b,c in R then prove that the roots of the equation (1)/(x-a)+(1)/(x-b)+(1)/(x-c)=0 are always real cannot have roots if a=b=c

If the difference of the roots of the equation x^(2)-bx+c=0 is equal to the differecne of the roots of the equation x^(2)-cx+b=0 and b!=c, then b+c= (i) 0 (ii) 2 (iii) 4 (iv) -4

Let a > 0, b > 0 & c > 0·Then both the roots of the equation ax2 + bx + c (A) are real & negative (C) are rational numbers 0 0.4 (B) have negative real parts (D) none

Number of distinct real roots of equation 3x^4+4x^3-12x^2+4=0

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

If 1,2,3 and 4 are the roots of the equation x^(4)+ax^(3)+bx^(2)+cx+d=0, then a+2b+c=

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