Question

Alpha and beta are zeros of polynomial F(y) = 6Y Square + Y -2 find the value of alpha / beta + beta / alpha

Answer 1

Let’s first solve the equation to get our zeroes of the equation i.e. alpha and beta.

6y2+y−2=06y2+y−2=0

6y2+4y−3y−2=06y2+4y−3y−2=0

2y(3y+2)−(3y+2)=02y(3y+2)−(3y+2)=0

which gives us two equations,

2y−1=0=>2y−1=0=>y=1/2(alpha)y=1/2(alpha)3y+2=0=>y=−2/3(beta)3y+2=0=>y=−2/3(beta)

So, the value of alpha/beta and beta/alpha will be -3/4 and -4/3, adding both of them gives the solution as -25/12.

Answer 2

6y2+y−2=06y2+y−2=0

6y2+4y−3y−2=06y2+4y−3y−2=0

2y(3y+2)−(3y+2)=02y(3y+2)−(3y+2)=0

which gives us two equations,

2y−1=0=>2y−1=0=>y=1/2(alpha)y=1/2(alpha)3y+2=0=>y=−2/3(beta)3y+2=0=>y=−2/3(beta)

So, the value of alpha/beta and beta/alpha will be -3/4 and -4/3, adding both of them gives the solution as -25/12.

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