Question

X²-6X+a;find the value of a if 3à+2ß is equal to 20

Answer 1

GIVEN
x²- 6x + a =0                                             

α and β are the zeroes of polynomial
α + β = coefficient with x/ coefficient with x² = 6 / 1 = 6......(i)
αβ= constant term / coefficient with x² = a / 1 = a............(ii)


3α + 2β = 20..........(iii)

solving (i) and (ii)
α + β = 6
α= 6 - β ......... (iv)

now we put the value of α  in (iii)
3(6 - β) + 2β = 20
18 - 3β + 2β = 20
18 - β = 20
-β = 20 - 18
-β = 2

⇒β = -2

 now put this value of β in (iv)
α = 6 - (-2)
α = 6 + 2
α= 8 

now put the value of α and β in (ii)
(8)(-2) = a
-16 = a