Question

If α and β are the zeros of the polynomial x2-6x+ a find the value of a if 3α+2β=20

Answer 1

a=-16 because one root alpha=8

Answer 2

Step-by-step explanation:

x² - 6x + a

a = 1    b = -6   c = a

α +β = -b/a = 6

αβ = c/a = a

3α + 2β = 20

3α = 20 - 2β  

α = (20 - 2β) / 3

α + β = 6

(20 - 2β)/3 + β = 6

multiplying by 3 on both sides

20 - 2β + 3β = 18

20 + β = 18

β = 18 - 20  

β = -2

α = (20 -2β)/3

α = (20 - 2 × -2)/3

α = (20 + 4)/3

α = 8

αβ =  a  

8 × -2 = a

a = -16

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