Question

Find the quabratic equation whose roots are (6+√5)and (6-√5)

Answer 1

Given:

• Roots/Zeroes are : (6 + √5 ) and ( 6 - √5 ) .

To find :

• Quadratic equation =? .

Solution :

As we know that :

• Quadratic equation

= x² - ( sum of Zeroes )x + product of zeroes .

• Sum of Zeroes = 6 + √5 + 6 - √5

=> sum of Zeroes = 12 .

• product of zeroes = (6+√5)(6-√5)

=> product of zeroes = 6² - √5²

=> product of zeroes = 36 - 5

=> product of zeroes = 31 .

Now , put the values in formula :

=> x² - 12x + 31

Hence , the quadratic equation is x² - 12x +31 .

Answer 2

Answer:

• Quadratic equation = x²-12x + 31 = 0

Step-by-step explanation:

Given that,

• Quabratic equation whose roots are (6+√5)and (6-√5).

Sum of roots = 6 + √5 + 6 - √5

➡ α + β = 12

Product of roots = (6 + √5) × (6 - √5)

[ °.° (a + b) (a - b) = a² - b² ]

➡ αβ = 6² - √5²

➡ αβ = 36 - 5

➡ αβ = 31

As we know that,

Quadratic equation = x²-(α + β)x+αβ = 0

[ Putting values ]

➡ Quadratic equation = x² - 12x + 31 = 0.