If `b^2<2a c` , then prove that `a x^3+b x^2+c x+d=0` has exactly one real root.

If |[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^2c^2, then the value of k is a b c b. a^2b^2c^2 c. b c+c a+a b d. none of these

If a^(2) + b^(2) + c^(3) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

Simplify (b^(2)+3b-28)/(b^(2)+4b+4)÷(b^(2)-49)/(b^(2)-5b-14)

Prove the identities: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2b^2c^2

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2b^2c^2