2. If (3, 2) are roots of x² + ax + Beta = 0 and (6, 1) are roots of x² + ax + b = 0, then find roots of
x + ax + b = 0.
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Correct option is
D
9,1
8,2 are the roots of x2+ax+β=0
⇒a=−(8+2)=−10
3,3 are the roots of x2+αx+b=0
⇒b=(3)(3)=9
x2+ax+b=0
⇒x2−10x+9=0
⇒x2−9x−x+9=0
⇒x(x−9)−1(x−9)=0
⇒(x−9)(x−1)=0
∴x=9orx=1
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