Question

Find a quadratic polynomial one of whose zeroes is (2 − √3) and sum of the zeroes is 4 ​

Answer 1

Answer:

x^2 - 4x + 1

Step-by-step explanation:

Since one root is 2 - sqrt(3), the other is 2 + sqrt(3)

[ Proof :

Since sum of the roots is equal to 4:

2 - sqrt(3) + 2 + sqrt (3) = 4 ]

Now , the factors of the polynomial is ( x - ( 2 - sqrt(3)) and ( x - ( 2 + sqrt(3))

To find the resulting polynomial, multiply the 2 factors.

( x - ( 2 - sqrt(3))*( x - ( 2 + sqrt(3))

[ Use the property (x-a)(x-b) = x^2 - (a+b)x + ab

= x^2 - ((2 - sqrt(3)) + ( 2 + sqrt (3)))x + (2 - sqrt(3))(2 + sqrt(3))

= x^2 - 4x + (2^2 - (sqrt(3))^2)

= x^2 - 4x + (4-3)

= x^2 - 4x + 1

Hope you understood my explanation.