Question

if alpha and beta are the Zeros of polynomial x^2-5x+c and alpha -beta =1,find alpha and beta​

Answer 1

Answer:

α = 3 and β = 2

Step-by-step explanation:

Given equation is-

$x^{2} - 5x + c = 0$

Comparing this equation with $ax^{2} +bx + c = 0$

We get,

a = 1, b = -5 and c = c (constant)

Given that-

α and β are the two roots of the equation and

α - β = 1           ---------------- 1

We know that-

The sum of roots of equation-

α + β = $-\dfrac{b}{a}$

        =  $-[\dfrac{-5}{1}]$

α + β = 5              -------------------- 2.

Adding equation 1 and 2 -

α - β = 1

α + β = 5    

             Adding    

2α = 6

α = 3

Put α = 3 in equation 1

3 - β = 1

β = 3 - 1

β = 2

Hence, α = 3 and β = 2