Question

factorise z²+3√3z-12 and verify relationship between zeroes and coefficient
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Answer 1

Answer:

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Answer 2

Given polynomial is ,

$z²+3\sqrt{3z} -12 \\\\\ = z² + 4\sqrt{3z} - \sqrt{3z} - 12 \\\\\ = (z+4\sqrt{3})(z- \sqrt{3})$

So , the zeroes are

$z+4\sqrt{3}=0 \implies z = -4\sqrt{3} \\\\\ z - \sqrt{3} = 0 \implies z = \sqrt{3}$

For verification ,

$\alpha + \beta = -4 \sqrt{3} + \sqrt{3} = -3\sqrt{3} = - {\frac{b}{a}} \\\\\ \alpha\beta = -12 = \frac {c}{a}$