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  • For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation. 2 sqrt 3

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation. 2 sqrt 3

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Answer.          \left [-3\sqrt{3}, \sqrt{3} \right ]    

Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.

Here, sum of zeroes -2\sqrt{3}

Product of zeroes = –9

Let p(x) is required polynomial

p(x) = x2 – (sum of zeroes)x + (product of zeroes)

=x^{2 }-(-2\sqrt{3})x+(-9)

=x^{2 } +2\sqrt{3}x+(-9)

p(x)=x^{2 } +2\sqrt{3}x+(-9)

Hence, x^{2 } +2\sqrt{3}x+(-9)  is the required polynomial

p(x)=x^{2 } +2\sqrt{3}x+(-9)

x^{2 } +3\sqrt{3}x-\sqrt{3}x+(-9)

x (x+3\sqrt{3})- \sqrt{3}(x + 3 \sqrt{3})

(x+3\sqrt{3})(x - \sqrt{3})

x =-3\sqrt{3}, \sqrt{3}  are the zeroes of p(x)

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