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Prove that th...

Question

Prove that the roots of the following quadratic equation has two real distinct roots.
$2 x^{2} - 6 x + 3 = 0$ .

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Solution

Given the quadratic equation is

$2 x^{2} - 6 x + 3 = 0$

Now discriminant of this equation is
$(- 6)^{2} - 4 \times 2 \times 3$

$= 36 - 24$

$= 12$ .

Since the discriminant of this equation is $> 0$ .

Then the roots of the quadratic equation are real and distinct.

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