Question

The quadratic equations with rational coefficients having √3/2 as a root is

Answer 1

SOLUTION

TO DETERMINE

The quadratic equations with rational coefficients having $\displaystyle \sf{ \frac{ \sqrt{3} }{2} }$ as a root

EVALUATION

Here it is given that a root of the required Quadratic equation is $\displaystyle \sf{ \frac{ \sqrt{3} }{2} }$

Now by the property of roots of a quadratic equation another root of the equation is

$\displaystyle \sf{ - \frac{ \sqrt{3} }{2} }$

Sum of the roots

$= \displaystyle \sf{ \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{2} }$

$= 0$

Product of the roots

$= \displaystyle \sf{ \frac{ \sqrt{3} }{2} \times - \frac{ \sqrt{3} }{2} }$

$\displaystyle \sf{ = - \frac{3}{4} }$

Hence the required Quadratic equation is

$\sf{ {x}^{2} -( \: Sum \: of \: the \: roots \: )x + \: Product \: of \: the \: roots = 0 }$

$\displaystyle \sf{ \implies \: {x}^{2} - 0.x - \frac{3}{4} = 0 }$

$\displaystyle \sf{ \implies \: {x}^{2} - \frac{3}{4} = 0 }$

FINAL ANSWER

The required Quadratic equation is

$\displaystyle \sf{ \: {x}^{2} - \frac{3}{4} = 0 }$

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