Question

it α= 2+✓3 and β=2-✓3the find the quadratic polynomial​

Answer 1

Answer:

the required quadratic polynomial​=x²+4x-1.

Step-by-step explanation:

here, α= 2+✓3 and β=2-✓3 are the two zeros of given polynomial.

then (α+β)=4 and αβ=2²-(√3)²=4-3=1

now , the required polynomial is given as,

x²+(α+β)x-αβ

=x²+4x-1

Answer 2

Answer:

x² -4x +1

Step-by-step explanation:

α= 2+✓3

x = 2+✓3

x - 2 - ✓3 = 0

β=2-✓3

x = 2 - ✓3

x - 2 + ✓3 = 0

So now we have the two factors if we multiply them we will get the answer,

(x -2 -✓3)×(x -2 +✓3)

x(x -2 +✓3) -2(x -2 +✓3) - ✓3(x -2 +✓3)

x² - 2x + ✓3x - 2x +4 -2✓3 -x✓3 +2✓3 - 3

Like terms together,

x²- 2x + ✓3x - 2x -x✓3 +4 -2✓3 +2✓3 -3

x² -4x +1

Here is your answer.