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 x^4-2x^2+4=0 forms a rectangle.

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.

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

If the both roots of the equation x^(2)-bx+c=0 be two consecutive integers, then b^(2)-4c equals

If the roots of the equation x^(2)-bx+c=0 are two consecutive integers, then b^(2)-4c is

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

If p is real, discuss the nature of the roots of the equation 4x^2+4px+p+2=0 , in terms of p.

(B) (2, 9/4) If two roots of the equation (a-1) (x^2 + x + 1 )^2-(a + 1) (x^4 + x^2 + 1) = 0 are real and distinct, then a lies in the interval

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0w h e r ea ,b ,c in Rdot