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Given that x1*x2 = - 3 calculate t if x^2 - 2x +t = 0

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leeaeel | Student, Undergraduate | (Level 2) Honors

Posted September 29, 2010 at 2:27 AM via web

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Given that x1*x2 = - 3 calculate t if x^2 - 2x +t = 0

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted September 29, 2010 at 2:31 AM (Answer #1)

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Being a quadratic, the equation has 2 roots.

We know, from enunciation that the product of the roots is -3.

We know also, using Viete's relations, that the product of the roots of the quadratic is the ratio: c/a.

We'll identify the coefficients c and a.

c = t

and

a = 1

So, x1*x2 = c/a

We'll sbstitute the product by the value -3 and the ratio by the identified coefficients.

-3 = t/1

So, t = -3.

The quadratic equation is:

x^2 - 2x -3= 0

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phucnguyen08 | Student, College Freshman | (Level 1) Honors

Posted September 29, 2010 at 12:18 PM (Answer #2)

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x1={-b-[b^2-4ac]^1/2}/2a= {2-(2^2-4*1*t)^1/2}/2*1

=[2-(4-4t)^1/2]/2

x2={-b+[b^2-4ac]^1/2}/2a={2+(2^2-4*1*t)^1/2}/2*1

=[2+(4-4t)^1/2]/2

x1*x2=-3           {[2-(4-4t)^1/2]*[2+(4-4t)^1/2}*1/4=-3

[2^2-[(4-4t)^1/2]^2}*1/4=-3

[4-(4-4t)]*1/4=-3             (4-4+4t)*1/4=-3

(0+4t)*1/4=-3              t=-3

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