Form the quadratic equation with rational coefficients whose one of the root is:
$2 + 3 \sqrt{5}$

x^{2} - 4 x - 41 = 0

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x^{2} + 4 x - 41 = 0

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x^{2} - 4 x - 45 = 0

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x^{2} + 4 x - 45 = 0

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Solution

The correct option is A $x^{2} - 4 x - 41 = 0$
If one of the roots of the equation is $2 + 3 \sqrt{5}$ other will be $2 - 3 \sqrt{5}$
Thus, sum of roots $= 4$
Product of roots $= (2 + 3 \sqrt{5}) (2 - 3 \sqrt{5})$ = $4 - 45 = - 41$
Hence, the equation can be written as $x^{2} - S x + P = 0$
$x^{2} - 4 x - 41 = 0$

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Form the quadratic equation with rational coefficients whose one of the root is:2+3√5

The correct option is A x2−4x−41=0If one of the roots of the equation is 2+3√5 other will be 2−3√5Thus, sum of roots =4Product of roots =(2+3√5)(2−3√5) = 4−45=−41Hence, the equation can be written as x2−Sx+P=0x2−4x−41=0

Form the quadratic equation with rational coefficients whose one of the root is:
$2 + 3 \sqrt{5}$