SOLUTION: Please solve: Given that the root of ax^2+bx+2=0 is 2-{{{sqrt(2)}}}, find the values of a and b, and the other root. (assume a and b are integers) Thanks.

Algebra.Com
Question 985658: Please solve:
Given that the root of ax^2+bx+2=0 is 2-, find the values of a and b, and the other root. (assume a and b are integers)
Thanks.

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!

One particular solution is the quadratic polynomial   
and the quadratic equation

= .

It has integer coefficients and the roots    and  .

Any other quadratic polynomial with the multiple coefficients,  like



with an integer  m  and the corresponding quadratic equation

=

is also the solution.


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Please solve:
Given that the root of ax^2+bx+2=0 is 2-, find the values of a and b, and the other root. (assume a and b are integers)
Thanks.
Since one root is: , then other root is: 
Sum of roots: = 4
Sum of roots: , so --------- eq (i)
Product of roots: -----> 4 - 2, or 2
Product of roots: , so ________________
---------- Substituting 1 for a in eq (i)
- b = 4 ---------- Cross-multiplying

RELATED QUESTIONS

Can you please solve this? I don't get the wording of the problem. Can you please show... (answered by josgarithmetic)
Question: Equation: x^3 + ax^2 +bx +a = 0 |a,b are real If x = 2+i is a... (answered by solver91311,ikleyn)
If one root of the equation ax^2+bx+c=0 is 2+√3 , then what is the other root if... (answered by ewatrrr)
If a,b,c i.e the coefficients of the quadratic equation ax^2+bx+c=0 are in A.P and the... (answered by ikleyn)
Given that f(x)=ax^2+bx+5, f(3)=2 and f'(3)=2 find the values of a and... (answered by Fombitz)
given that x=3+i is a root of p(x)=3x^4+ax^3+34x^2+bx-20 find the value of a and b if... (answered by greenestamps)
Find the values of a and b that result in the given sum. [(a+1)x^2 + bx + 2] +... (answered by jim_thompson5910)
Please solve this problem! I don't understand how to solve it. Given that x^2-2x-5=0... (answered by josgarithmetic)
The graph of y=ax^2+bx+c passes through the points (0,-9) and (-1,9). Given that the... (answered by greenestamps)