Question

if alpha and beta are the zeroes of the polynomial x2-5x+k, such that alpha-beta=1, find the value
plz solve by discriminate method​

Answer 1

Answer:

x²-5x+k

α+β=5--eq1

α-β=1(given)--eq2

Add eq1 and eq2, we get

2β=4

β=4/2

β=2

Substitute β=2 in eq2

α-β=1

α-2=1

α=1+2

α=3

αβ=k--eq3

αβ=3×2=6(given)--eq4

From eq1 and eq2, we get

k=6

Or

x²-5x+k

a=1, b=(-5), c=k

Discriminant=0

b²-4ac=0

(-5)²-4(1)(k)=0

25-4k=0

(-4k)=(-25)

4k=25

k=25/4

k=6.25

I have solved it by both the methods.