Question

Write a quadratic polynomial whose sum and product of the zeroes are –3/4 and 5/6 respectively.​

Answer 1

Answer:

x^2 +3x/4 + 5/6

Step-by-step explanation:

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Answer 2

$\sf\underline{Answer:}$

Let the zeroes of the quadratic polynomial be alpha and beta

$\alpha + \beta = \frac{ - 3}{4}$

$\alpha \beta = \frac{5}{6}$

Quadratic polynomial is given by,

$k[ {x}^{2} - ( \alpha + \beta)x + \alpha \beta ]$

$k[ {x}^{2} - \frac{ - 3}{4} x + \frac{5}{6} ]$

$k[ \frac{ {12x}^{2} + 9x + 10}{12} ]$

k can be any number and is a constant, but let us consider k = 12

$12 {x}^{2} + 9x + 10$

The quadratic polynomial would be either

${x}^{2} + \frac{ 3}{4} x + \frac{5}{6}$ or $12 {x}^{2} + 9x + 10$

Have a good afternoon!