Question

find a quadratic polynomial each with the given numbers as the sum and the product of its zeroes. (i) 5/12,-1/6​

Answer 1

Step-by-step explanation:

this might help u ..

here is a pic for ur refrence

Answer 2

Step-by-step explanation:

Given:

Sum of zeros : 5/12

Product of zeros: -1/6

To find: Find the quadratic polynomial.

Solution:

Let a quadratic polynomial have zeros $\alpha\:and\:\beta$ then it is given by

$\bold{ {x}^{2} - ( \alpha + \beta )x + \alpha \beta}$

Here,

Sum of zeros

$\alpha + \beta = \frac{5}{12}$

Product of zeros

$\alpha \beta = \frac{ - 1}{6}$

Therefore quadratic polynomial is

${x}^{2} - \frac{5}{12} x +\left( \frac{ - 1}{6} \right) \\ \\ or \\ \\ {x}^{2} - \frac{5}{12} x - \frac{1}{6} \\ \\ or \\ \\ \frac{12 {x}^{2} - 5x -2 }{12} = 0 \\ \\ 12 {x}^{2} - 5x - 2 = 0$

Final answer:

The polynomial is

$\bold{\red{12 {x}^{2} - 5x - 2 = 0 }}$

whose sum of zeros is 5/12 and product of zeros are -1/6.

Hope it helps you.

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