Exemplar problems XXIII — task. Mathematics CBSE, Class 10.

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Find the zeroes of the polynomial \(2s^2 - (1 + 2 \sqrt{2})s + \sqrt{2}\), and verify the relation between the coefficients and the zeroes of the polynomial.

Answer:

The zeroes are

and

Sum of the zeroes \(=\)

Product of the zeroes \(=\)

Answer variants:

\frac{- constant}{coefficient of s^{2}} = \frac{\sqrt{2}}{2}

\frac{- coefficient of s}{coefficient of s^{2}} = \frac{1 + 2 \sqrt{2}}{2}

\(s = \sqrt{2}\)

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

\(s = \frac{1}{2}\)

\frac{- coefficient of s}{coefficient of s^{2}} = \frac{- (1 + 2 \sqrt{2})}{2}

\(s = \frac{3}{\sqrt{2}}\)

\frac{constant}{coefficient of s^{2}} = \frac{\sqrt{2}}{2}

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42. Exemplar problems XXIII

Exercise condition: