1.

Find quardtic equation whose one of zeroes is 2+ ✓3​

Answer»

Step-by-step explanation:

If 2+sqrt(3) is a ZERO, so is the conjugate 2-sqrt(3) .

Also, if a is a zero, then (x-a) is a factor, thus the factors of the quadratic are:

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

Multiplying we get:

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

Adding LIKE terms:

x^2-4x+1

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The monic quadratic polynomial with rational coefficients is:

x^2-4x+1

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** CHECKING we can use the quadratic FORMULA to FIND the roots(zeros):

x=(4+-sqrt(16-4(1)(1)))/(2(1))

=(4+-sqrt(12))/2

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

=2+-sqrt(3)

and we see that 2+sqrt(3) is a zero.


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