The correct option is D None of these
Equation of line AB is (y−0)=4−03−1(x−1)⇒y=2(x−1)
Solving line AB with the given circle,
x2+4(x−1)2=4⇒x=0,85 ⇒y=−2,65
Thus P=(0,−2) and Q=(85,65)
Also A=(1,0),B=(3,4)
Now, BP=√32+62=√45=3√5,PA=√12+22=√5∴α=3
and, BQ=√(3−85)2+(4−65)2=7√5
QA=√(1−85)2+(0−65)2=3√5∴β=73
Now α+β=163,α.β=7
Hence quadratic equation having roots α,β is given by,
3x2−16x+21=0