Question

@ganeshie8 @robtobey

Answer 1

D two negative roots

Answer 2

For finding the answer we calculate the discernment of the equation after determining a, b and c.
The polynomial is :
\[4x^2+10x+6\]
So :
\[a=4~,~b=10~\text{and }~ c=6.\]
So :
\[\Delta=b^2-4ac=10^2-4\times4\times6=100-96=4>0\]
So the polynomial has two distinct real roots.
The roots are :
\[x_1=\frac{-b+\sqrt\Delta}{2a}=\frac{-10+\sqrt4}{8}=\frac{-10+2}{8}=-1<0\\x_2=\frac{-b-\sqrt\Delta}{2a}=\frac{-10-\sqrt4}{8}=\frac{-10-2}{8}<0\]
So the two roots are both negative !