Question

find the quadratic equation whose zeros are (5-√2)(5+√2)​

Answer 1

Solution :

Here, given that two zeroes of the quadratic equation are

• (5 - √2)
• (5 + √2)

As we know that formula for finding a quadratic equation is

=> x² - (α + β)x + αβ

Where

• (α + β) = sum of zeroes
• αβ = product of zeroes

Let

• α = (5 - √2)
• β = (5 + √2)

Finding sum of zeroes :

➟ (5 - √2) + (5 + √2)

➟ 5 - √2 + 5 + √2

➟ 5 + 5

➟ 10

Finding product of zeroes :

➟ (5 - √2) (5 + √2)

➟ (5)² - (√2)²

➟ 25 - 2

➟ 23

Now, put the values in the formula.

➟ x² - (α + β)x - αβ

➟ x² - (10)x - 23

➟ x² - 10x - 23

• Hence, the quadratic equation is x² - 10x - 23.