Given in the picture that [tex]D=b^{2} -4ac[/tex].
(a) Express b in terms of a, c and D.
[tex]b=\sqrt{D-4ac}[/tex]
(b) Find the values of b when a=2, c=-2 and D=81.
[tex]b=\sqrt{65}[/tex]
By seeing the question we can say that the [tex]b^{2} -4ac[/tex] is in the quadratic formula.
We know the general Quadratic Equation is [tex]ax^{2}+bx+c=0[/tex].
The solution to find the root of the Quadratic Equation is Quadratic Formula: [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex].
The whole solution is depend on [tex]b^{2} -4ac[/tex]. The team is called discriminant.
(a) Given that,
[tex]D=b^{2} -4ac[/tex]
[tex]b^{2}=D +4ac\\[/tex]
Taking square root on both sides.
[tex]\sqrt{b^{2} } =\sqrt{D+4ac}\\ b=\sqrt{D+4ac}\\[/tex]
Therefore, [tex]b=\sqrt{D-4ac}[/tex]
(b) Given that,
a=2,c=-2 and D=81
[tex]b=\sqrt{D+4ac}\\[/tex]
[tex]b=\sqrt{81+4(2)(-2)}\\[/tex]
[tex]b=\sqrt{81-16}[/tex]
[tex]b=\sqrt{65}[/tex]
Therefore, [tex]b=\sqrt{65}[/tex]
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