Question Two quadratic functions are given. ()=−2−2+6 ()=22+5+3 Identify all values of x, to the nearest tenth, for which f (x) = g(x). A. –2.7 B. –1.8 C. –0.6 D. 0.4 E. 4.1 F. 5.1 G. 7.0

Answer: [tex](a)\ x = 0.4\ or\ (d)\ x = -2.7[/tex] Step-by-step explanation: Given [tex]f(x) = -x^2 – 2x +6[/tex] [tex]g(x) = 2x^2 + 5x + 3[/tex] Required Find x if [tex]f(x) = g(x)[/tex] The above implies that: [tex]-x^2 -2x +6 = 2x^2 + 5x +3[/tex] Collect like terms [tex]2x^2 + x^2 + 5x + 2x + 3 – 6 = 0[/tex] [tex]3x^2 + 7x – 3 = 0[/tex] Using quadratic formula, we have; [tex]x = \frac{-b \± \sqrt{b^2 – 4ac}}{2a}[/tex] Where [tex]a=3; b=7; c=-3[/tex] [tex]x = \frac{-7 \± \sqrt{7^2 – 4*3*-3}}{2*3}[/tex] [tex]x = \frac{-7 \± \sqrt{49+ 36}}{6}[/tex] [tex]x = \frac{-7 \± \sqrt{85}}{6}[/tex] [tex]x = \frac{-7 \± 9.22}{6}[/tex] Split [tex]x = \frac{-7 + 9.22}{6}\ or\ x = \frac{-7 – 9.22}{6}[/tex] [tex]x = \frac{2.22}{6}\ or\ x = \frac{-16.22}{6}[/tex] [tex]x = 0.4\ or\ x = -2.7[/tex] — approximated Log in to Reply

Answer:[tex](a)\ x = 0.4\ or\ (d)\ x = -2.7[/tex]

Step-by-step explanation:Given[tex]f(x) = -x^2 – 2x +6[/tex]

[tex]g(x) = 2x^2 + 5x + 3[/tex]

RequiredFind x if [tex]f(x) = g(x)[/tex]

The above implies that:[tex]-x^2 -2x +6 = 2x^2 + 5x +3[/tex]

Collect like terms[tex]2x^2 + x^2 + 5x + 2x + 3 – 6 = 0[/tex]

[tex]3x^2 + 7x – 3 = 0[/tex]

Using quadratic formula, we have;[tex]x = \frac{-b \± \sqrt{b^2 – 4ac}}{2a}[/tex]

Where[tex]a=3; b=7; c=-3[/tex]

[tex]x = \frac{-7 \± \sqrt{7^2 – 4*3*-3}}{2*3}[/tex]

[tex]x = \frac{-7 \± \sqrt{49+ 36}}{6}[/tex]

[tex]x = \frac{-7 \± \sqrt{85}}{6}[/tex]

[tex]x = \frac{-7 \± 9.22}{6}[/tex]

Split[tex]x = \frac{-7 + 9.22}{6}\ or\ x = \frac{-7 – 9.22}{6}[/tex]

[tex]x = \frac{2.22}{6}\ or\ x = \frac{-16.22}{6}[/tex]

[tex]x = 0.4\ or\ x = -2.7[/tex]— approximated