if `alpha` and `beta` are the root of the quadratic polynomial `f(x) = x^2-5x+6` , find the value of `(alpha^2 beta + beta^2 alpha)`

Options

A. 20
B. 30
C. 50
D. none of these

Answer

B

Explanation

Again, it is given that the point P,Q and R are collinear.
`implies PQ=lamdaQR`
`implies 15t(4hati-3hati)=lamda[(1-t)(hati+hatj)-60thatj]`
`implies=lamda[(1-t)hati+(1-61t)hatj]`
`implies (45t)/(t-1)=(60t)/(1-61t)`
`implies (3t)/(t-1)=(4t)/(1-61t)`
`implies3(1-61t)=4(t-1)`
`implies 3-183t=4t-4implies 187t=7`
`therefore t=(7)/(187)`.