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
Question
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