Answer:
[tex]x \approx 1.16[/tex]
Step-by-step explanation:
a.
To find the values of m and n, we have to first expand [tex](x + m)^2 + n[/tex] :
[tex](x + m)^2 + n[/tex]
⇒ [tex]x^2 + 2mx + m^2 + n[/tex]
[tex]f(x) = x^2 + 4x - 6[/tex]
Now compare the coefficients of the x-terms:
• [tex]2mx = 4x[/tex]
⇒ [tex]\bf m = 2[/tex]
• [tex]m^2 + n = -6[/tex]
⇒ [tex]2^2 + n = -6[/tex]
⇒ [tex]n = -10[/tex]
b.
[tex]x^2 + 4x - 6 = 0[/tex]
∴ [tex](x + 2)^2 - 10 = 0[/tex]
⇒ [tex](x + 2)^2 = 10[/tex]
⇒ [tex]x + 2 = \sqrt{10}[/tex]
⇒ [tex]x = \sqrt{10} -2[/tex]
⇒ [tex]x \approx 1.16[/tex]
