Question

A) 1

b) 5
c) -1/2
d) sqrt. 3

not multiple choice, those are all the problems I need answered

thanks

Answer 1

a) x² − √3 x + ½

b) 5x² − 5√3 x + ⁵/₂

c) -½ x² + ½√3 x − ¼

d) √3 x² − 3 x + ½√3

Explanation:

Write the factored form of the quadratic:

(x − (√3 + 1)/2) (x − (√3 − 1)/2)

Distribute using FOIL (first, outer, inner, last):

x² − (√3 − 1)/2 x − (√3 + 1)/2 x + (√3 + 1)/2 (√3 − 1)/2

Combine like terms:

x² − ((√3 − 1)/2 + (√3 + 1)/2) x + (√3 + 1)(√3 − 1)/4

Simplify:

x² − ((√3 − 1 + √3 + 1)/2) x + (√3 + 1)(√3 − 1)/4

x² − √3 x + (√3 + 1)(√3 − 1)/4

x² − √3 x + (3 − √3 + √3 − 1)/4

x² − √3 x + ½

Now multiply by each new coefficient.

b) 5x² − 5√3 x + ⁵/₂

c) -½ x² + ½√3 x − ¼

d) √3 x² − 3 x + ½√3