Question

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

Answer 1

Step-by-step explanation:

Polynomial   P(x) = x² - 6 x + a

Given  α and  β  are the roots.     To find a , if 3 α + 2 β = 20.  ---(1)

From the quadratic expression:

    α + β = 6       ---(2)

    and   α β = a  --- (3)

Multiply equation (2) by 2 and subtract from (1) to get:

    α = 20 -12 = 8

Substitute this value in(2) to get:    

     β = 6-8 = -2   

Substitute these in (3) to get:    a = α β = -16.

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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