The equation whose roots are 1 3 + 2 and 1 3 - 2 is - Vidyadip

MCQ

The equation whose roots are $\frac{1}{{3 + \sqrt 2 }}$and $\frac{1}{{3 - \sqrt 2 }}$ is

✓
$7{x^2} - 6x + 1 = 0$
B
$6{x^2} - 7x + 1 = 0$
C
${x^2} - 6x + 7 = 0$
D
${x^2} - 7x + 6 = 0$

✓

Answer

Correct option: A.

$7{x^2} - 6x + 1 = 0$

a
(a) The required equation is

${x^2} - \left( {\frac{1}{{3 + \sqrt 2 }} + \frac{1}{{3 - \sqrt 2 }}} \right)x + \frac{1}{{3 + \sqrt 2 }} \times \frac{1}{{3 - \sqrt 2 }} = 0$

$ \Rightarrow {x^2} - \left( {\frac{6}{7}} \right)x + \frac{1}{7} = 0 \Rightarrow 7{x^2} - 6x + 1 = 0$

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