Question

find a quadratic polynomial whose sum and product of zeroes are -2√3 , -9

Answer 1

Answer :

If α and β be zeroes of any quadratic polynomial, the polynomial be

f(x) = x² - (α + β)x + αβ

In this problem, given that -

α + β = - 2√3 and αβ = - 9

Therefore, the required polynomial be

f(x) = x² - (- 2√3)x + (- 9)

⇒ f(x) = x² + 2√3x - 9,
which is the required polynomial.

#MarkAsBrainliest

Answer 2

$\alpha + \beta = ( - 2 \sqrt{3)} \\ \alpha \times \beta = ( - 9) \\ {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta \\ {x}^{2} - ( - 2 \sqrt{3} )x + ( - 9) \\ {x}^{2} + 2 \sqrt{3} x - 9$
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