Question

find a quadratic polynomial for which the sum and the product of zeroes are
and root 5 and 3/4 respectively​

Answer 1

Let the zeroes be $\alpha \: and \beta$

respectively

Sum of the zeroes:

$\alpha + \beta$= 5 + 3/4

= 23/4

Product of the zeroes:

$\alpha × \beta$= 5 × 3/4

= 15/4

Therefore, f(x) = $x^2 - ( \alpha + \beta)x + (\alpha \beta)$

= $x^2 - (23/4)x + 15/4$

= 1/4 {4x² - 23x + 15}

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