The correct option is D roots are negative, if all three of a,b,c have the same sign and Δ>0
ax2+bx+c=0; a,b,c∈R
If b=c=0
⇒ax2=0
⇒x=0,0
If c=0, then
ax2+bx=0
⇒(ax+b)x=0
⇒x=0,−ba
For real roots, Δ=b2−4ac≥0
Let roots are m and n
m+n=−ba, mn=ca
Since, roots are negative,
Therefore, both ba and ca are positive.
ba→+ve⇒a,b→+ve or a,b→−ve
ca→+ve⇒a,c→+ve or a,c→−ve
⇒ Either a,b,c→+ve or a,b,c→−ve
Hence, if roots are negative, then all three of a,b,c have the same sign.