Quadratic equation corresponding to the roots 2+{5}{ and }2-{5} is

Correct Answer is : x2−4x−1=0x² - 4x - 1 = 0x2−4x−1=0

Correct Answer is : x2−4x−1=0x² - 4x - 1 = 0x2−4x−1=0

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RRB Group-D Model Paper 13 with answers for online practice

Question : 15 of 100

Marks: +1, -0

2+\sqrt{5}\text{ and }2-\sqrt{5}

Solution:

Given:

Two roots are

2+\sqrt{5}\text{ and }2-\sqrt{5}

Concept used:

The quadratic equation is:

x^{2}

- (Sum of roots)x + Product of roots = 0

Calculation:

Let the roots of the equation be A and B.

A =

2 + \sqrt{5}\text{ and }B = 2 - \sqrt{5}

⇒ A + B =

2 + \sqrt{5} + 2 - \sqrt{5} = 4

⇒ A × B =

(2 + \sqrt{5})(2 - \sqrt{5}) = 4 - 5 = -1

Then equation is

∴

x^{2} - 4x - 1 = 0

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