Question

2-3x+2 and r- 51+ have a root in common?
hat is the sum of all possible values of k for which the polynomials
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Answer 1

Answer:

What is the sum of all possible values of k for which the polynomials x^2 -3x=2 and x^2-5x=k have a root in common?

Solution: x^2 -3x=2, or

x^2–3x-2 = 0

x1 = [3+(9+8)^0.5]/2

= [3+√17]/2

x2 = [3-√17]/2

x^2-5x=k.

If x1 = [3+√17]/2, then k1 = [3+√17]^2/4 - 5[3+√17]/2

= [3+√17]*[[3+√17]/4 -5[3+√17]/2

= [3+√17]*(-19)[3+√17]/8

=[3+√17]^2*(-19/8).

If x2 = [3-√17]/2, then k2 = [3-√17]^2/4 - 5[3-√17]/2

=[3-√17]^2*(-19/8).

The sum of the values of k = k1 + k2: (-19/8)[(3+√17)^2 + (3-√17)^2].