If the product of x + a and x + b is x^2 + 3x + 6 what is a and b

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The product of the terms x + a and x + b is x^2 + 3x + 6.

`(x + a)(x + b) = x^2 + (a + b)*x + ab`

`x^2 + (a + b)*x + ab = x^2 + 3x + 6`

=> `a + b` = 3 and `ab = 6`

Substitute a = 3 - b in a*b = 6

=> (3 - b)*b = 6

=> 3b - b^2 = 6

=> b^2 - 3b + 6 = 0

=> b1 = `(3 + sqrt(9 - 24))/2 = 3/2 + i*sqrt 15/2` and `b2 = 3/2 - i*sqrt 15/2`

a1 = `3/2 - i*sqrt 15/2` and `a2 = 3/2 + i*sqrt 15/2`

The value of a and b is `{3/2 - i*sqrt 15/2, 3/2 + i*sqrt 15/2}` and `{3/2 + i*sqrt 15/2, 3/2 - i*sqrt 15/2}`

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salonigaba | Student, Grade 11 | (Level 1) Salutatorian

Posted on

Hi,

the value of a and will be: (x+a)(x+b)=x2+xb+xa+ab=x2+x(a+b)+ab

a+b=3

ab=6

by puting the of a(a=3-b)in ab=6

a={(3/2)-iota*sqrroot of15/2,(3/2)+iota*sqrroot of15/2}

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