suppose α and β are the roots of a quadratic equation. it is known that α^2+β^2=9 and (α+3β)(3α+β)=-13.
find the quadratic equationform a quadratic equation with roots α^2+1 and β^2+1
點解AND 點做??
HELP ME!!
maths f.4 (10PTS)
2010-10-10 8:39 am
回答 (2)
2010-10-10 9:09 am
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------有錯請指正-------
2010-10-10 01:10:02 補充：
B part equation is x^2 -11x+26=0
2010-10-10 9:26 am
Q.1
(α+3β)(3α+β)=-13
3(α^2+β^2)+10αβ=-13
27+10αβ=-13
αβ=-4
α^2+β^2=9
(α+β)^2-2αβ=9
α+β=1
-b/a=1
c/a=-4
The equation is x^2-x-4=0.
Q.2
The roots of x^2-x-4=0 are (1+sqt17)/2 and (1-sqt17)/2 respectively
The roots of the new equation are (11+sqt17)/2 and (11-sqt17)/2 respectively
The equation is x^2-11x+26=0.
(α+3β)(3α+β)=-13
3(α^2+β^2)+10αβ=-13
27+10αβ=-13
αβ=-4
α^2+β^2=9
(α+β)^2-2αβ=9
α+β=1
-b/a=1
c/a=-4
The equation is x^2-x-4=0.
Q.2
The roots of x^2-x-4=0 are (1+sqt17)/2 and (1-sqt17)/2 respectively
The roots of the new equation are (11+sqt17)/2 and (11-sqt17)/2 respectively
The equation is x^2-11x+26=0.
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