The sum of the roots of \(\sqrt2\)x² - 2\(\sqrt5\)x + \(\sqrt3\) = 0 is _________.

Question

Question

This question was previously asked in

RRB Group D 30 Aug 2022 Shift 3 Official Paper

Answer 1

Concept used:

If a quadratic equation (ax² + bx + c = 0)

Then, sum of roots = -b/a

Where b = coefficient of x

a = coefficient of x²

Calculation:

Here, we have \(\sqrt2\)x² - 2\(\sqrt5\)x + \(\sqrt3\) = 0

Now, divide the equation by \(\sqrt2\)

⇒ x² - \(\sqrt2\) × \(\sqrt5\) x + \(\sqrt3\over\sqrt2\) = 0

Now, this is in the form of ax² + bx + c = 0

Where , a= 1 , b = -\(\sqrt{10}\) , c = \(\sqrt3\over \sqrt2\)

Now, as we know that sum of roots = -b/a

⇒ -b/a = - ( - \(\sqrt{10}\) ) = \(\sqrt{10}\)

Hence, the required sum of roots is \(\sqrt{10}\).