Q7. Find the quadratic equation whose roots are 2+√3 and 2-√3.
Answers
Answer:
Requiredequation:
x
2
−4x+1=0
Step-by-step explanation:
\begin{lgathered}Let\:\alpha\:and\:\beta \:are\\ roots \: of \:a \: quadratic\: equation\end{lgathered}
Letαandβare
rootsofaquadraticequation
\begin{lgathered}Given \: \alpha= 2+\sqrt{3}\\and \: \beta = 2-\sqrt{3}\end{lgathered}
Givenα=2+
3
andβ=2−
3
\begin{lgathered}i) Sum \:of \: roots\\ = \alpha+\beta\\=2+\sqrt{3}+2-\sqrt{3}\\=4\end{lgathered}
i)Sumofroots
=α+β
=2+
3
+2−
3
=4
\begin{lgathered}ii) Product \:of \: roots\\ = \alpha \beta\\=(2+\sqrt{3})(2-\sqrt{3})\\=2^{2}-(\sqrt{3})^{2}\\=4-3\\=1\end{lgathered}
ii)Productofroots
=αβ
=(2+
3
)(2−
3
)
=2
2
−(
3
)
2
=4−3
=1
\begin{lgathered}We\:know\:that \\ Equation \:of \: a \: Quadratic\\eqution \: whose \: roots \:are\:\alpha \\and \: \beta\:is \:x^{2}-(\alpha+\beta)x+\alpha \beta =0\end{lgathered}
Weknowthat
EquationofaQuadratic
equtionwhoserootsareα
andβisx
2
−(α+β)x+αβ=0
Now,Requiredequation:
x
2
−4x+1=0
Answer: l hope this is a correct answer
Explanation:
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