Question

write a quadratic polynomial, sum of whose zeros is 2√2 and their product is 7√3​

Answer 1

Answer:

Given that sum of zeros i.e

$s = 2 \sqrt{2}$

And product of zeros i.e.

$p = 7 \sqrt{3}$

We know that

quadratic polynomial with sum of zeros s and product of zeros p is of the form

$x {}^{2} -sx + p$

So reqrd. Polynomial is:-)

${x}^{2} - 2 \sqrt{2} \: x + 7 \sqrt{3}$

VERIFICATION

$SUM \: \: OF \: \: ZEROS = \dfrac{ - (coeff. \: of \: x)}{coeff. \: of \: {x}^{2} } \\ \\ = \frac{ - ( - 2 \sqrt{2} )}{1} \\ \\ = 2 \sqrt{2}$

$PRODUCT \: \: OF \: \: ZEROS = \dfrac{constant}{coeff. \: of \: {x}^{2} } \\ \\ = \frac{7 \sqrt{3} }{1} \\ \\ = 7 \sqrt{3}$