Answer:
The solution follows below
Step-by-step explanation:
12·x²+70·x+a²+1=0
Let's find the discriminant
D=4900-12*4*(a²+1)=4900-48(a²+1) <4900 for any a
So √D<70 (1) for any a
first root X1= (-70-√D)/24<0 so -70-√D<0
second root x2=(-70+√D)/24<0 so -70+√D<0 (√D<70 look to inequality (1))
=> Both roots are negative for any a.
