Find a quadratic polynomial each with the given numbers as the zeros o

1.	Find a quadratic polynomial each with the given numbers as the zeros of the polynomials. √3,3√3
Answer» <P>Given that zeros are $\sf\alpha = \sqrt{3} \\ \\ \sf \beta = 3 \sqrt{3}$ $\sf SUM \: OF \: ROOTS = s = \alpha + \beta \\ \\ = \sf \sqrt{3} + 3 \sqrt{3} \\ \\ \sf = 4 \sqrt{3} \\ \\ \sf PRODUCTS \: OF \: ROOTS = p = \alpha \beta \\ \\ = \sf \sqrt{3} \times 3 \sqrt{3} = 9$ We KNOW that quadratic POLYNOMIAL WHOSE sum is roots is s and product of roots is p is given by $\sf {x}^{2} - sx + p$ So REQUIRED Polynomial is $\sf {x}^{2} - 4 \sqrt{3} \:x + 9$

Find a quadratic polynomial each with the given numbers as the zeros of the polynomials. √3,3√3

Answer»

<P>Given that zeros are

$\sf\alpha = \sqrt{3} \\ \\ \sf \beta = 3 \sqrt{3}$

$\sf SUM \: OF \: ROOTS = s = \alpha + \beta \\ \\ = \sf \sqrt{3} + 3 \sqrt{3} \\ \\ \sf = 4 \sqrt{3} \\ \\ \sf PRODUCTS \: OF \: ROOTS = p = \alpha \beta \\ \\ = \sf \sqrt{3} \times 3 \sqrt{3} = 9$