Question

Prove that the equation 12x2+70x+a2+1=0 for any value of a does not have any positive roots. I need help ASAP! Please someone Help

Answer 1

The solution follows below

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.