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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 2s ^2

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

2s^{2}-(1+2\sqrt{2})s+\sqrt{2}

Answers (1)

Answer. \left [\frac{1}{2}, \sqrt{2} \right ]

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

2s^{2}-(1+2\sqrt{2})s+\sqrt{2} = 0

2s^{2}-s-2\sqrt{2}s+\sqrt{2}=0

s(2s-1)-\sqrt{2}(2s-1)=0

(s-\sqrt{2})(2s-1)=0

2s – 1 = 0                                (s-\sqrt{2})=0

s=\frac{1}{2}                                 s=\sqrt{2}

Hence, \left [\frac{1}{2}, \sqrt{2} \right ]  are the zeroes of the polynomial

Here, a = 2, b=-(1+2\sqrt{2}), c= \sqrt{2}

Sum of zeroes =\frac{-b}{a}=\frac{-(-1+2\sqrt{2})}{2}=\frac{1+2\sqrt{2}}{2}

Here, \frac{1}{2}+\sqrt{2}=\frac{1+2\sqrt{2}}{2}

Product of zeroes =\frac{c}{a}=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}

Here, 1\times \frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}}=\frac{c}{a}

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