Find the zeroes of the quadratic polynomial $x^{2} + 5 x + 6$ and verify the relationship between its zeroes and coefficients.

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Solution

Factorise the given polynomial
$x 2 + 5 x + 6 = x 2 + 2 x + 3 x + 6$
$= x (x + 2) + 3 (x + 2)$
$= (x + 2) (x + 3)$
For finding zeroes of the polynomial, equate the given polynomial to zero,
$(x + 2) (x + 3) = 0$
So, $x = - 2$ and $x = - 3$
Therefore, the zeroes of the given polynomial are -2, -3

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