Jay T. answered • 11d

Retired Engineer/Math Tutor

The quadratic formula states that the roots of any quadratic equation, ax^{2}+bx+c = 0 are given by

Roots = __-b ± √(b__^{2}__-4ac)__

2a

In this problem, we have x^{2} + 7x + 1 = 0

a = 1

b=7

c=1

Plugging these into the quadratic formula, we have

Roots = __-7 ± √(7__^{2}__ – 4(1)(1)__

2(1)

= -3.5 ± ½√45__ __

__ __

So

Roots are -3.5 + ½√45 and -3.5 - ½√45 or ≈ - 6.854 and -0.146