Question

21. If alpha and bita are the zeros of the polynomial f(x) = x2 - 5x + k such that
alpha-bita = 1, find the value of k.
​

Answer 1

Answer:

Given if αβ are zeroes of quadratic polynomial

f(x)=x

2

−5x+k (1)

& α−β=1

& α−β=5 & αβ = k

we know (α+β)

2

−(α−β)

2

=4αβ

25−1=4αβ

αβ=

4

24

=6

∴ value of k = αβ=6.

Step-by-step explanation:

I hope this may help you

Answer 2

Answer:

k = 6

Step-by-step explanation:

$\alpha-\beta =1\\or, (\alpha-\beta)^2 =1\\or, (\alpha+\beta)^2- 4\alpha\beta =1\\or, (\frac{-b}{a})^2 - \frac{4c}{a} =1\\or, (-(-5)/1)^2 - (4k/1) = 1\\or, 25 - 4k = 1\\or, 4k = 24\\or, k=6$