Question

find the polynomial whose zeroes are

a) 3+ underroot 2 and 3 - underroot 2

Also show the working.

Answer 1

Hey there!

Sum of roots = 3 + √2 + 3 - √2 = 6 .
Product of roots = ( 3 + √2 ) (3 - √2 ) = 9 - 2 = 7 .

Now,
We know that,
Quadratic equation =>
x² - ( sum of roots) x + product of roots = 0 .

x² - ( 6)x + 7 = 0 .

Hence, x²-6x+7 = 0 is the required quadratic equation.

Answer 2

Answer:

Sum of roots = 3 + √2 + 3 - √2 = 6 .

Product of roots = ( 3 + √2 ) (3 - √2 ) = 9 - 2 = 7 .

Now,

We know that,

Quadratic equation =>

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

x² - ( 6)x + 7 = 0 .

Hence, x²-6x+7 = 0 is the required quadratic equation.

Step-by-step explanation: