Prove that the equation `x^(2)(a^(2)b^(2))+2x(ac+bd)+(c^(2)+d^(2))=0` has no real root if `adnebc`.

For a , b , c non-zero, real distinct, the equation, (a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0 has non-zero real roots. One of these roots is also the root of the equation :

If the equation (b^2 + c^2) x^2 -2 (a+b) cx + (c^2 + a^2) = 0 has equal roots, then

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.

Without actually solving show that the equation x^(4)+2x^(3)-2=0 has only one real root in the interval (0,1) .

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

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.

Let a , ba n dc be the three sides of a triangle, then prove that the equation b^2x^2+(b^2=c^2-alpha^2)x+c^2=0 has imaginary roots.

If the roots of the equation (c^(2)-ab)x^(3)-2(a^(2)-bc)x+b^(2)-ac=0 are real and equal prove that either a=0 (or) a^(3)+b^(3)+c^(3)=3"abc" .

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these