Question

if alpha and beta are zeros of polynomial x square - 5 x + c and alpha-beta=1 find c​

Answer 1

x2-5x+c

Here, a=1, b=-5 and c=k

Now, α+ β = -b/a= -(-5)/1= 5

α*β = c/a= k/7= k

Now,α - β =1

Squaring both sides, we get,

(α - β)2=12

⇒ α2 + β2 - 2αβ = 1

⇒ (α2 + β2 + 2αβ) - 4αβ = 1

⇒ (α +β)2 -4αβ =1

⇒ (5)2-4k=1

⇒ -4k= 7-25

⇒ -4k= -24

⇒ k=6 So the value of c is 6.

Answer 2

Step-by-step explanation:

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.