Question

alpha and beta are the zeros of the polynomial FX equal to x square - 5 x + K such that Alpha minus beta equal to 1 find the value of k​

Answer 1

Answer:

Given that:

$\tt{\alpha - \beta = 1}$ ...(1)

We know that:

$\tt{\alpha + \beta = \frac{-b}{a} = 5}$ ...(2)

(1) - (2)

=》 $\tt{\beta = 2}$

=》 $\tt{\alpha = 3}$

We know that:

$\tt{\alpha\beta = \frac{c}{a}}$

=》 $\tt{2 \times 3 = k}$

=》 $\tt{k = 6}$

Answer 2

Answer : k = 6

Step by step explanation :

We know that ,

Sum of zeroes : -b/a

α + β = 5.. (1)

Product of zeroes = c/a

αβ = k.. (2)

Given that,

α - β = 1.. (3)

Thus,

Adding (1) and (3)

α + β = 5

+ α - β = 1

_____________

=⟩⟩ 2α = 6

α = 3

Similarly,

α + β = 5

3 + β = 5

β = 2

Now, From (2)

αβ = k

3 × 2 = k

6 = k

Thus, The value of k is 6.