Question

If alpha and beta are zeroes of polynomial x2-5x+k such that alpha-beta=1.find k​

Answer 1

Step-by-step explanation:

a=alpha

b=beta

p(x)=x^2-5x+k

so,

a-b=1----------(1)

a+b=5---------(2)

Now we will solve,

a-b=1

a+b=5 (-b+b will be cut)

----------

2a=6

----------

so,

2a=6

a=3

to find b,take eqn (1)

a-b=1

3-b=1

-b=1-3

-b=-2 (minus and minus will be cut)

b=2

.:k=ab(alpha × beta)

k=3×2

k=6

Answer 2

k=6 is the answer

here , a=1,b=-5,c=k

α+β= -b/a

= -(-5/1)

= 5/1

= 5

α*β= c/a

= k/1

= k

now, α-β= 1

squaring both the sides, we get,

(α-β)²= (1)²

α²+β²-2αβ = 1

(α²+β²+2αβ)-4αβ= 1

(α+β)²-4αβ = 1

(5)²-4k= 1

25-4k =1

-4k=1-25

-4k= -24

k= -24/-4

k= 24/4

k = 6 (answer)

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