Question

Determine the nature of the root of the quadratic equation 3x²–3√6x+2=0
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Answer 1

Comparing the equation to $ax^2 + bx + c=0$, we have:

$a=3,b=3\sqrt6=\sqrt54,c=2$

$b^2-4ac = 54 - 4*3*2\\=54 - 24\\= 30$

Thus we have $b^2-4ac > 0$

Hence the Roots are Real and Distinct(Non-Equal).

Since $b$ is irrational, the roots will also be irrational.

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