If the roots of the equation `x^2-2a x+a^2-a-3=0` are real and less than 3, then (a)`a<2` b. `2<-alt=3` c. `34`

The number of real roots of the equation |x|^(2)-3|x|+2=0 is

Let a ,b , c be the sides of a triangle, where a!=b!=c and lambda in R . If the roots of the equation x^2+2(a+b+c)x+3lambda(a b+b c+c a)=0 are real. Then a. lambda<4/3 b. lambda>5/3 c. lambda in (1/3,5/3) d. lambda in (4/3,5/3)

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" .

For a alt=0, determine all real roots of the equation x^2-2a|x-a|-3a^2=0.

Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0.

The number of real solution of the equation x^(2)-3|x|+2=0 is

The sum of real roots of the equation |x-2|^2+|x-2|-2=0 is (A) 4 (B) 1 (C) 2 (D) -2

If c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0

If roots of equation x^2+2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

Using differentiation method check how many roots of the equation x^3-x^2+x-2=0 are real?