Question

Q.3.Find the quadratic equation whose roots are (6 + V5) and
(6-√5)​

Answer 1

Given,

The two roots of a quadratic equation = (6+✓5) and (6-✓5)

To find,

The actual quadratic equation.

Solution,

We can easily form a quadratic equation if it's two roots are given, by using the following mathematical formula.

Quadratic equation :

x²-(sum of two roots)x + (product of roots) = 0

Now,

Sum of roots = (6+✓5+6-✓5) = 12

Product of roots = (6+✓5) (6-✓5) = (6)²-(✓5)² = 36-5 = 31

Quadratic equation :

x² - 12x + 31 = 0

[By putting the values.]

Hence, the quadratic equation will be x² - 12x + 31 = 0