Question

3. If a and Bare the zeros of the polynomial f(x) = x2.5x + k such that a- B = 1, find k​

Answer 1

Answer:

The value of k is 6

Step-by-step explanation:

Given:

$f(x)=x^2-5x+k$

sum of the zeros $=\frac{-(-5)}{1}$

$a+b=5$..................(1)

Also,

$a-b=1$.................(2)

Adding (1) and (2)

2a=6

a=3

put a=3 in (1) we get

3+b=5

b=2

product of the zeros$=\frac{k}{1}$

$\implies\:ab=k$

$\implies\:(3)(2)=k$

$\implies\:k=6$