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  • Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials: v ^2

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

v^{2}+4\sqrt{3}v-15

Answers (1)

Answer. -5\sqrt{3},\sqrt{3}

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

v^{2}+4\sqrt{3}v-15=0

v^{2}+5\sqrt{3}v-\sqrt{3}v-15=0

v(v+ 5\sqrt{3})-\sqrt{3}(v+5\sqrt{3})=0

(v+ 5\sqrt{3})(v-\sqrt{3})=0

(v+ 5\sqrt{3}) =0                             (v-\sqrt{3})=0

v =-5\sqrt{3}                                             v =\sqrt{3}

Hence, -5\sqrt{3},\sqrt{3}  are the zeroes of the polynomial

Here, a = 1, b = 4\sqrt{3} , c = –15

Sum of zeroes =\frac{-b}{a}=\frac{-4\sqrt{3}}{1}=-4\sqrt{3}

Here, -5\sqrt{3}+\sqrt{3}=-4\sqrt{3}=\frac{-b}{a}

Product of zeroes =\frac{c}{a}=-15

Here, -5\sqrt{3}\times \sqrt{3}=-15=\frac{c}{a}

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