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

1.	The quadratic equations with rational coefficients having √3/2 as a root is
Answer» 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 $\sf{ {<klux>X</klux>}^{2} -( \: Sum \: of \: the \: roots \: )x + \: Product \: of \: the \: roots = 0 }$ $\displaystyle \sf{ \implies \: {x}^{2} - 0.x - \frac{3}{4} = 0 }$ $\displaystyle \sf{ \implies \: {x}^{2} - \frac{3}{4} = 0 }$ FINAL ANSWER The required Quadratic equation is $\displaystyle \sf{ \: {x}^{2} - \frac{3}{4} = 0 }$ ━━━━━━━━━━━━━━━━ Learn more from Brainly :- 1. write a quadratic polynomial sum of whose zeroes is 2 and product is -8 brainly.in/question/25501039 2. solve for x: x + 1/x = 3, x not equal to 0 brainly.in/question/4991905