Question

find the zeroes of the polynomialx²-3 find the relationship between zeroes and confident ​

Answer 1

Answer:

$p(x) = x ^2 - 3\\\\0 = (x + \sqrt3)(x - \sqrt3)\\\\\therefore x + \sqrt3= 0 \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ x - \sqrt3 = 0\\\therefore x = - \sqrt3 \ \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ x = \sqrt3\\\\Let \ the \ zeroes \ be \ \alpha = \sqrt3 \ \ and \ \beta = - \sqrt3$$Sum \ of \ zeroes = \frac{-b}{a}\\\\\alpha + \beta = \frac{0}{1}\\\\\sqrt3 \times (- \sqrt3) = \frac{0}{1}\\\\\sqrt3 -\sqrt3 = \frac{0}{1}\\\\0 = 0\\\\\\Product \ of \ zeroes = \frac{c}{a}\\\\\alpha \times \beta = \frac{-3}{1}\\\\\sqrt3 \times (- \sqrt3) = \frac{-3}{1}\\\\-3 = \frac{0}{1}\\\\-3 = -3\\\\Thus \ the \ relationship \ between \ the \ zeroes \ and \ the \ co-efficients \ is \ verified.$

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