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Q.

If R is the circum radius and r, r1, r2, r3 are inradius and ex-radii of the triangle then the roots of the equation x3(4R+r)x2+s2xrs2=0 are

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a

r1r2,r2r3,,r3r1

b

r1, r2, r3

c

r1r2, r2r3, r3r1

d

r1+r2, r2+r3, r3+r1

answer is B.

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Detailed Solution

Letα,β,γarerootsofx3(4R+r)x2+s2xrs2=0α+β+γ=4R+rWeknowthatr1+r2+r3=4R+randαβγ=rs2r1,r2,r3areroots

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If R is the circum radius and r, r1, r2, r3 are inradius and ex-radii of the triangle then the roots of the equation x3–(4R+r)x2+s2x–rs2=0 are