Quadratic equation corresponding to the roots \(2 + \sqrt 5 \) and \(2 - \sqrt 5\) is

Question

Question

Answer 1

Given:

Two roots are 2 + √5 and 2 - √5.

Concept used:

The quadratic equation is:

x2 - (Sum of roots)x + Product of roots = 0

Calculation:

Let the roots of the equation be A and B.

A = 2 + √5 and B = 2 - √5

⇒ A + B = 2 + √5 + 2 - √5 = 4

⇒ A × B = (2 + √5)(2 - √5) = 4 - 5 = -1

Then equation is

∴ x2 - 4x - 1 = 0

F1 Shailesh 17.5.21-Pallavi D2 (1)

For a quadratic equation, ax² + bx + c = 0,

Sum of the roots = (-b/a) = 4/1

Product of the roots = c/a = -1/1

Then, b = -4

So, the sign of coefficient of x is negative.