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The solutions of the quadratic equation \(x^2+px+q=0\) are obtained by adding \(5\) to each of the solutions of \(x^2-4x+2=0\). Find the value of \(3p+q\).

 Apr 30, 2022
 #1
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Call the roots of x^2  - 3x + 2 =  0     =  m   ,  n

The roots of   x^2   -3x  + 2  = 0  sum to   -(-3)/1  =   3

The product  of the roots = 2

So mn   = 2

 

So  (m + 5) + (n + 5)  =  (m + n) + 10   = 3 + 10 =  13  ....so p = -p/ 1   =  -13  

And the product of these roots = q 

So

(m + 5)(n + 5)  =  q

mn + 5(m+n)  + 25  = q

2 + 5 (3) + 25  = q

42  =  q

 

So

 

3p + q   =

 

3 (-13) + 42   =    3

 

 

cool cool cool

 Apr 30, 2022
 #2
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thank you!

 Apr 30, 2022

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