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Grade 11Algebra

If p,q are roots of the quadratic equation x^2-10rx-11s=0 and r,s are roots of x^2-10px-11q=0, then find the value of p+q+r+s.

Profile image of Vedang Sarangi
8 Years agoGrade 11
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1 Answer

Profile image of Arun
8 Years ago
Dear Vedang
 
p + q = 10r
r + s = 10p
hence
p+ q+ r+ s = 10 (p+ r)              …...(i)
Now if we add both the quadratic equations
-22*121-99(p+r)=0, So p+r=121 or -22, As for p=-22, we get p=r, so reject this2(p+r)
hence
p + r = 121
so from (i) equation
p +q+r+s = 10 (p +r) = 1210