CBSE · Class 10 · Mathematics · PolynomialsFind the zeroes of the polynomial $p(x) = x^2 - 3$ and verify the relationship.

To find the zeroes of $p(x) = x^2 - 3$, we set $p(x) = 0$, which gives $x^2 - 3 = 0$. We can rewrite this using the difference of squares identity as $(x - \sqrt{3})(x + \sqrt{3}) = 0$. This yields two possible solutions: $x = \sqrt{3}$ and $x = -\sqrt{3}$. Thus, the zeroes of the given quadratic polynomial are $\sqrt{3}$ and $-\sqrt{3}$. The sum of zeroes is $\sqrt{3} + (-\sqrt{3}) = 0$, and the product is $(\sqrt{3})(-\sqrt{3}) = -3$, which perfectly matches the coefficients of the standard form $1x^2 + 0x - 3$.