Question

if alpha and beeta are zeroes of the quadratic polynomial x^2-6x+a,find the value if a if 3 alpha+2 beeta=20

Answer 1

Hey there !!!!!!!!

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p(x) = x²-6x+a it has α,β as zeroes of polynomial

We know that if p(x) = ax²+bx+c has α,β as its roots then 

α+β = -b/A and αβ=c/A

So comparing  p(x) = x²-6x+a with Ax²+bx+c

A=1 b=-6 and c =  a

α+β = 6   αβ = a

According to question  3α+2β= 20---Equation 1

α+β = 6

Multiplying with 2

2α+2β = 12---Equation 2

Solving Equation 1 and equation 2

Equation 1 - Equation 2

α = 20- 12

α=8

Sub α=8 in equation 2

2*8+2*β=12

2β=12-16

β= -2  α=8

But αβ= a

      αβ = -16

a= -16

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Hope this helped you.....................