Let `(a_(1),a_(2),a_(3),a_(4),a_(5))` denote a re=arrangement of (3,-5,7,4-9), then `a_(1)x^(4)+a_(2)x^(3)+a_(3)x^(2)+a_(4)+a_(5)=0` has

Options

A. at least two real roots
B. all four real roots
C. only imaginary roots
D. None of these

Answer

A

Explanation

Let f(x)= `a_(1)x^(4)+a_(2)x^(3)+a_(3)x^(2)+a_(4)+a_(5)`
Than,
`f(1)=a_(1)+a_(2)+a_(3)+a_(4)+a_(5)=0`
`:. X=1` is a root of f(x)=0.
Since f(x) is an even degree equation. So, it has at least one more real root. Hence, f(x)=0 has at least two real roots.