What is the value of the following determinant? `Delta=|[4,a, b+c],[4,b, c+a],[4,c, a+b]|`

If a+b+c=4 and ab+bc+ca=0 , then what is the value of the following determinant? |(a, b, c),(b, c, a),(c, a, b)|

If a, b, c are positive and unequal show that value of the determinant Delta=|[a, b, c],[ b, c, a],[ c, a, b]| is negative.

What is the value of following determinant ? |(a-b, b-c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|

Write the value of the following determinant |(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|

If a,b,c are unequal then what is the condition that the value of the following determinant is zero Delta =|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|

If a,b,c are unequal then what is the condition that the value of the following determinant is zero Delta =|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|

Without expanding show that the following determinants vanish |(4,a,b+c),(4,b,c+a),(4,c,a+b)|

If a , b , c are unequal , what is the condition that value of the following determinant is zero ? Delta=|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|

What is the value of the determinant |(a-b,b+c,a),(b-c,c+a,b),(c-a,a+b,c)| ?

If a, b, c are positive and unequal, show that value of the determinant Delta=|a b c b c a c a b| is negative.