Question

x²+5x+k if a and b the zeros of polynomial of a-b=1

Answer 1

$\huge\tt\underline\blue{solution}$

equation

x²+5x+k

a+b=-b/a.

a+b= -5. eq (1)

and

a*b=c/a

a*b=k eq (2)

a-b=1. (given)

(a-b)²=1. { (A-B)²=A²+B²-2AB}

both side square

a²+b²-2ab=1

a²+b²-2ab+2ab=1+2ab.

add (2ab) both side

(a+b)²-4ab=1. [ (A+B)²=A²+B²+2AB ]

from equation (1) and (2)

(-5)²-4k=1

25-4k=1

-4k= - 24

4k=24

k=6

$\huge\tt\underline\pink{answer :k=6}$

$\huge\tt\underline\blue{Thanks}$

hope its helpful