Answer:
a) we get value of n: n=10.7 or n=1.2 when d=30
b) we get value of n: n=9.6 or n=2.3 when d=20
Step-by-step explanation:
a) solve for n When do= 30
Put d= 30 in the given equation:
[tex]d = n^2-12n + 43[/tex]
[tex]30=n^2-12n+43\\n^2-12n+43-30=0\\n^2-12n+13=0\\[/tex]
Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=1, b=-12 and c=13
[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(13)}}{2(1)}\\n=\frac{12\pm\sqrt{144-52}}{2}\\n=\frac{12\pm\sqrt{92}}{2}\\n=\frac{12\pm9.59}{2}\\n=\frac{12+9.59}{2} , n=\frac{12-9.59}{2}\\n=10.7 , n=1.2\\[/tex]
So, we get value of n: n=10.7 or n=1.2
b) solve for n when d=20
[tex]d=n^2-12n+43\\20=n^2-12n+43\\n^2-12n+43-20=0\\n^2-12n+23=0\\[/tex]
Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=1, b=-12 and c=23
[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(23)}}{2(1)}\\n=\frac{12\pm\sqrt{144-92}}{2}\\n=\frac{12\pm\sqrt{52}}{2}\\n=\frac{12\pm7.21}{2}\\n=\frac{12+7.21}{2} , n=\frac{12-7.21}{2}\\n=9.6 , n=2.3\\[/tex]
So, we get value of n: n=9.6 or n=2.3
