Question

Find a quadratic equations whose zeroes are3+√2 and 3-√2

Answer 1

Answer:

The required quadratic equation is x² - 6x + 7.

Step-by-step explanation:

Given :

The zeroes of the polynomial are (3+√2) and (3-√2)

To find :

the quadratic equation

Solution :

We can find the quadratic equation from the relation between zeroes and coefficients.

Sum of zeroes :

= 3 + √2 + 3 - √2

= 6

Product of zeroes :

= (3+√2) (3-√2)

= 3(3-√2) + √2(3-√2)

= 9 - 3√2 + 3√2 - 2

= 9 - 2

= 7

The quadratic equation is of the form :

x² - (sum of zeroes)x + (product of zeroes)

So, substituting the values,

=> x² - 6x + 7

Hence, the required polynomial is x² - 6x + 7.