Question

form the quadratic equation whose roots are 7±2√5​

Answer 1

Given:

The roots 7±2√5​.

To find:

The quadratic equation of the given roots.

Solution:

If we have two roots A and B then the equation of the polynomial is given by:

• x²+(A+B)x+AB

here we have

• A = 7+2√5
• B = 7-2√5

So,

• A+B = 7+2√5+7-2√5 = 14
• AB = (7+2√5)(7-2√5) = 7²-(2√5)² = 49 -20 = 29

Putting these values in the equation we get:

• x² + 14x +29 = 0

The quadratic equation of the given roots is x² + 14x +29 = 0