Prove that the equation `x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0` has no real root, if `a d!=bc dot`

Prove that the equation x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0 has no real root, if a d!=b c .

If (a^2+b^2)x^2+2(ac+bd)x+c^2+d^2=0 has no real root

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 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

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 (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

If a, b, c, d are real numbers such that (a+2c)/(b+3d)+(4)/(3)=0 . Prove that the equation ax^(3)+bx^(2)+cx+d=0 has atleast one real root in (0, 1).

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

Check that if the roots of the equation (a^2+b^2)x^2+2x(ac+bd)+c^2+d^2=0 are real,whether they will be equal