Question

if alpha and beta are the zeroes of the polynomial x2-5x+k, such that alpha-beta=1, find the value of k

Answer 1

Answer:

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Step-by-step explanation:

α= alpha

β= beta

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

so,

α-β=1-----------(1)

α+β=5---------(2)

now we will solve

α-β=1

α+β=5        (-β+β will be cut)

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2α=5

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so,

2α=6

α=3

to find β,

take equation (1)

α-β=1

3-β=1

-β=1-3

-β=-2  (minus and minus will be cut)

β=2

∴K= αβ (alpha x beta)

k=3x2

k=6

Answer 2

Answer:

k=6

Step-by-step explanation:

alpha and beta are zeros of the polynomial f(x)=x^2-5x+k.

let alpha=a &beta=b

a+b=-(-5/1)=5;ab=k/1=k

Now, a-b=1

squaring both sides

(a-b)^2=1

(a+b)^2-4ab=1

25-4k=1

4k=24

k=6.