Question

if alpha and beta are zeroes of polynomial x²- 5x+k such that alpha - beta =1. Find the value of k.
plz answer fast.. it's urgent..

Answer 1

Hola Estimado !
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let α and β are two zeros of given polynomial 
Polynomial = x²-5x+k 
also α-β      = 1
        α         =  1+β
we know c/a = product of zeros 
                 k  =  αβ
                 k  =  (1+β )(β)     ∵[α=1+β]
                 k  =  β+β²______________(1)
also, -b/a = sum of zeros 
             5 = α+β
             5 = β+1+β
             5 = 2β+1
             4 = 2β
             β = 2
put value of β in equation 1
we get ,
k= β+β²
k= 2+2²
k= 2+ 4
k= 6 
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Answer 2

Given that ;

• p(x) = x² - 5x + k
• from p(x) , a = 1 , b = -5 , c = k
• α - β = 1
• so , α = 1 + β

To find :

• value of k ?

Solution ;-

we know that

α+β = -b/a

so ,

1 + β + β = -(-5)/1 = 5

2β = 5-1 = 4

so , β = 2

so , α = 1 + β = 1+2 = 3 , α = 3

then ,

we know that , αβ = c/a

then , (2)(3) = k/1 = k

k = 6

• value of k = 6