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

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Find the zeroes of the polynomial \(v^2 + 4 \sqrt{3} v - 15\), 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:

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

\(v = 5 \sqrt{3}\)

\(v = -\sqrt{3}\)

\frac{- constant}{coefficient of v^{2}} = - 15

\(v = \sqrt{3}\)

\frac{- coefficient of v}{coefficient of v^{2}} = 4 \sqrt{3}

\frac{- coefficient of v}{coefficient of v^{2}} = - 4 \sqrt{3}

\frac{constant}{coefficient of v^{2}} = - 15

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43. Exemplar problems XXIV