Question

If the difference of zeros of polynomials, p(x) = x2

– 5x + k is 1, find k.​

Answer 1

Correct Question :-

If α and β are the zeroes of polynomials

P(x) = x^2 - 5x + k = 1 then find the value of K

Solution :-

Here,

Given polynomial is x^2 - 5x + k

compare this equation with the general form of quadratic equation ax^2 + bx + c = 0

Therefore,

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

Now,

Sum of zeroes = α + β = -b/a

Subsitute the required values

α + β = -(-5)/1

α + β = 5

Product of zeroes = αβ = c/a

Subsitute the required values,

αβ = k/1

αβ = k

Now,

According to the question,

α - β = 1.

α = 1 + β eq( 1 )

α + β = 5. eq( 2 )

1 + β + β = 5

2β = 5 - 1

β = 4/2 = 2

Now, Subsitute the value of β in eq( 2 )

α + 2 = 5

α = 5 - 2

α = 3

Here,

αβ = k

Subsitute the value of α and β here

3 * 2 = k

6 = k

Hence, The value of k is 6 $.$

Answer 2

Answer:

k=6

Step-by-step explanation:

Given if αβ are zeroes of quadratic polynomial

f(x)=x²−5x+k

& α−β=1

& α−β=5

& αβ = k

We know,(α+β)²−(α−β)²=4αβ

25−1=4αβ

αβ=24/4

=6

∴ value of k = αβ=6.