Question

If a and B are the zeroes of polynomial p(x) = x2 - 5x + 6 then find the value of a +B - 3 ab. And 1/a + 1/b
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Answer 1

-13 and 5/6

Step-by-step explanation:

a and b are zeroes of x²-5x+6

a=1,b=-5,c=6

multiplication of roots=c/a

ab=6/1=6

addition=-b/a= -(-5)/1

=5

we have to find :-

1. a+b-3ab

=>5-3(6)

=>5-18=-13

2. 1/a + 1/b

=>5/6

Hence, required answer is -13 and 5/6

Answer 2

Step-by-step explanation:

${x}^{2} - 5 x + 6 \\ \alpha + \beta = \frac{ - ( - 5)}{1} \\ \alpha + \beta = 5 \\ \alpha \beta = 6 \\ \\ \alpha + \beta - 3 \alpha \beta = 5 - 3 \times 6 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5 - 18 \\ \: \: \: \: \: \: \: \: \: \: \: \: = - 13 \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \beta + \alpha }{ \alpha \beta } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{5}{6}$