75
Find the zeroes of the quadratic polynomial $x^2 - 15$ and verify the relationship between the zeroes and the coefficients of the polynomial.
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Let $P(x) = x^2 - 15$
$= (x - \sqrt{15})(x + \sqrt{15})$
$\therefore$ Zeroes of $P(x)$ are $-\sqrt{15}$ and $\sqrt{15}$
Verification-
Sum of zeroes = $-\sqrt{15} + \sqrt{15} = \frac{0}{1} = \frac{- \text{coefficient of } x}{\text{coefficient of } x^2}$
Product of zeroes = $-\sqrt{15} \times \sqrt{15} = -15 = \frac{-15}{1} = \frac{\text{constant term}}{\text{coefficient of } x^2}$
$= (x - \sqrt{15})(x + \sqrt{15})$
$\therefore$ Zeroes of $P(x)$ are $-\sqrt{15}$ and $\sqrt{15}$
Verification-
Sum of zeroes = $-\sqrt{15} + \sqrt{15} = \frac{0}{1} = \frac{- \text{coefficient of } x}{\text{coefficient of } x^2}$
Product of zeroes = $-\sqrt{15} \times \sqrt{15} = -15 = \frac{-15}{1} = \frac{\text{constant term}}{\text{coefficient of } x^2}$