Verified answer

x^2 + 7x - 1

a = 1, b = 7, c = -1

D = b^2 - 4ac = 7^2 - 4*1*(-1) = 54

As we can see [tex]\sqrt{D}[/tex] is not a complete root, factorising the equation after getting its roots will be much easier

[tex]x = \frac{-b + \sqrt{D}}{2a}[/tex]  and  [tex]\frac{-b- \sqrt{D}}{2a}[/tex]

[tex]x = \frac{-7 + 3\sqrt{6}}{2}[/tex]  and [tex]\frac{-7 - 3\sqrt{6}}{2}[/tex]

⇒  [tex]x - \frac{-7+ 3\sqrt{6}}{2} = 0[/tex]  and  [tex]x - \frac{-7- 3\sqrt{6}}{2} = 0[/tex]

∴ [tex]x + \frac{7 - 3\sqrt{6}}{2}[/tex]  and  [tex]x + \frac{7 + 3\sqrt{6}}{2}[/tex] are the factors of the equation, i.e.,

Answer:

x^2 + 7x - 1 = [tex](x + \frac{7 - 3\sqrt{6}}{2})(x + \frac{7 + 3\sqrt{6}}{2})[/tex]

I suggest you to recheck the question

Hope I helped ☺☻

Answer:

The answer is -