Question

Find a quadratic polynomial whose zeros are √15 and -√15

Answer 1

$\alpha = { \sqrt{15} } \\ \beta = - \sqrt{15} \\ \\ p(x) = k[ {x}^{2} - ( \alpha + \beta )x + \alpha \beta] \\ p(x) = k [{x}^{2} - ( \sqrt{15} - \sqrt{15} )x + ( \sqrt{15} )( - \sqrt{15} )] \\ p(x) = k[ {x}^{2} - 15 ]\\ for \: k = 1 \\ p(x) = {x}^{2} - 15$

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Answer 2

Zeroes:

α = √15

β = -√15

Now,

equation = (x + α)(x - β)

=> (x + √15)(x -√15))

=> x² - √15x + √15x - 15

=> x² - 15

Hence, The quadratic equation in standard form is:

x² + 0x - 15