If `a ,b ,c in R ,` then find the number of real roots of the equation `Delta =|[x, c,-b],[-c, x, a], [b,-a,x]|=0`

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.

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 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

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

If a ,b ,c are distinct positive numbers, then the nature of roots of the equation 1//(x-a)+1//(x-b)+1//(x-c)=1//x is Option a) all real and is distinct Option b) all real and at least two are distinct Option c) at least two real Option d) all non-real

If a,b and c are distinct positive real numbers in A.P, then the roots of the equation ax^(2)+2bx+c=0 are

If a ,b ,c are three distinct positive real numbers, the number of real and distinct roots of a |x^2|+2b|x|-c=0 is a. 0 b. 4 c. 2 d. none of these

Solve the equation |a-x c b c b-x a b a c-x|=0w h e r ea+b+c!=0.

Let a ,b ,c be real numbers with a!=0a n dl e talpha,beta be the roots of the equation a x^2+b x+c=0. Express the roots of a^3x^2+a b c x+c^3=0 in terms of alpha,betadot