Math, asked by Ekam737, 1 month ago

28. What is the value of k, if one root of the quadratic equation x² - 4x +k=0
is 2+√3?
(A) - 1 (B) 1
(C) 2
(D) – 2

Answers

Answered by Sanskarbro2211
3

Given :-

x^2 - 4x +k=0

\alpha =2+\sqrt{3}

Required to find :-

\beta =?\\k=?

Procedure :-

Let us take the following condition

x^2 - 4x +k=0x^2-(\alpha +\beta )x+\alpha \beta =0

Now from above,

\alpha +\beta =4\\\alpha \beta =k

Now let us square the second condition and substitute first condition wherever required.

(\alpha +\beta )^2=\alpha ^2+\beta ^2+2\alpha \beta\\16=4+3+4\sqrt{3} +\beta +4\beta +2\beta \sqrt{3}\\16=7+4\sqrt{3} +\beta^2 +4\beta +2\beta \sqrt{3}\\4\sqrt{3} +\beta^2 +4\beta +2\beta \sqrt{3}-9=0

You then need to use   \beta =\frac{-b ± \sqrt{b^2-4ac} }{2a}  (Angstrom symbol must be omitted as it came due to some error).

Substitute in condition  \alpha \beta =k to get k value.

Do it yourself and you would be able to do such problems yourself with no effort.

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