Question

find a polynomial in x if it's zeroes are -√3 and √3 .​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{It is given that a polynomial's roots are }-\sqrt3 \text{ and }\sqrt3$

$\implies \text{The polynomial's factors are }(x+\sqrt3)\text{ and }(x-\sqrt3)$

       $\text{We know that a polynomial is a product of its factors}$

$\implies \text{The polynomial} = (x+\sqrt3)(x-\sqrt3)$

       $\text{We know that, }(a+b)(a-b) = a^{2} - b^{2}$

$\implies \text{The polynomial} = (x)^{2} - (\sqrt3)^{2}$

$\implies \boxed{\text{The polynomial} = x^{2} - 3}$