Answer:
Step-by-step explanation:
44). Given function is,
f(x) = 7x² - 3x - 1
x intercept means value x at f(x) = 0.
Therefore, for f(x) = 0
7x² - 3x - 1 = 0
By quadratic formula,
x = [tex]\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
= [tex]\frac{3\pm \sqrt{(-3)^2-4(7)(-1)}}{2(7)}[/tex]
= [tex]\frac{3\pm \sqrt{37}}{14}[/tex]
Therefore, x - intercepts are x = [tex]\frac{3- \sqrt{37}}{14},\frac{3+\sqrt{37}}{14}[/tex] ≈ -0.22, 0.65
45). f(x) = x² + 4x + 7
For x intercepts, f(x) = 0
x² + 4x + 7 = 0
By quadratic formula,
x = [tex]\frac{-4\pm \sqrt{16-28}}{2}[/tex]
= [tex]\frac{-4\pm \sqrt{-12} }{2}[/tex]
= (-2 ± i[tex]\sqrt{12}[/tex])
Since, x intercepts are imaginary, there are no x-intercepts.
46). Given formula for the projectile is,
s = 96t - 16t²
For s = 96 ft
96 = 96t - 16t²
6 = 6t - t²
0 = -t² + 6t - 6
t² - 6t + 6 = 0
By quadratic formula,
t = [tex]\frac{6\pm \sqrt{6^2-4(1)(6)}}{2(1)}[/tex]
t = [tex]\frac{6\pm \sqrt{36-24}}{2}[/tex]
t = [tex]\frac{6\pm \sqrt{12} }{2}[/tex]
t = (3 ± √3) ≈ 1.27 seconds, 4.73 seconds
