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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: 4x^ 2

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

4x^{2}+5 \sqrt{2}x-3

Answers (1)

Answer.  \left [\frac{-3}{\sqrt{2}}, \frac{1}{2 \sqrt{2}} \right ]

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

4x^{2}+5 \sqrt{2}x-3 = 0

4x^{2}+6 \sqrt{2}x-\sqrt{2}x-3=0

2\sqrt{2}x (\sqrt{2}x+3)-1 (\sqrt{2}x+3)=0

(\sqrt{2}x+3)(1-2\sqrt{2}x)

(\sqrt{2}x+3) =0                             (1-2\sqrt{2}x) =0

x=\frac{-3}{\sqrt{2}}                                           x=\frac{1}{2\sqrt{2}}             

Hence, \left [\frac{-3}{\sqrt{2}}, \frac{1}{2 \sqrt{2}} \right ]  are the zeroes of the polynomial

Here, a = 4, b = 5\sqrt{2} , c = –3

Sum of zeroes =\frac{-b}{a}=\frac{-5\sqrt{2}}{4}=\frac{-5}{2\sqrt{2}}

Here, \frac{-3}{\sqrt{2}}-\frac{1}{2\sqrt{2}}=\frac{-6+1}{2\sqrt{2}}=\frac{-5}{2\sqrt{2}}=\frac{-b}{a}

Product of zeroes =\frac{c}{a}=\frac{-3}{4}

Here, \frac{-3}{\sqrt{2}}\times \frac{1}{2\sqrt{2}}=\frac{-3}{4}=\frac{c}{a}

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