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Mathematics · Polynomials · NCERT Examples

Example 3

A complete, independently verified solution for NCERT Example 3.

Mathematics · Chapter 2 · NCERT Examples

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NCERT Example

Example 3

quadratic polynomials · zeroes and coefficients

Find the zeroes of the polynomial x² − 3 and verify the relationship between the zeroes and the coefficients.

Solution

x2−3=(x−3)(x+3)x^2-3=(x-\sqrt3)(x+\sqrt3)

The zeroes are √3 and −√3.

3−3=0=−ba\sqrt3-\sqrt3=0=-\frac{b}{a}
(3)(−3)=−3=ca(\sqrt3)(-\sqrt3)=-3=\frac{c}{a}

Final answer

The zeroes are √3 and −√3; their sum is 0 and product is −3.