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1. IF A + B + C = 0 then the quadratic equation 3ax² + 2bx + c = 0 has,< how to solve>

(a) At least one root in (0,1)

(b) One root in (2,3) and other in (-2,-1)

(c) imaginary roots

(d) None of these

Hello student,
Please find the answer to your question below
Let f(x)=ax³+bx²+cx+d
then f(0)=0 and f(1)=a+b+c=0
also f is differentiable on R
By rolles theorem there exists a root(p) in (0,1) such that f¹(p)=0
p=(0,1) such that 3ap²+2bp+c=0