Question

Q.2If α and β are the zeroes of the polynomial f(x)=x 2 -5x+k such that α-β=1 then find
the value of k.

Answer 1

ANSWER:

The value of K= 6

GIVEN:

α and β are the zeroes of the polynomial f(x)=x^2 -5x+k such that α-β=1

TO FIND:

Value of K

SOLUTION:

We know that:

$α + β = \frac{( - b)}{a} \\ α \times β = \frac{c}{a}$

where; (a= coefficient of x^2) . (b= coefficient of x)

( c= constant term)

$f(x) = x {}^{2} - 5x + k \\ : here \: \: \: α + β = \frac{ - ( - 5)}{1} \\ \implies \: α + β = 5 \\ \\ \impliesα \times β = \frac{k}{1} \\ \implies \: αβ = k$

α + β= 5 ..........(i)

α - β= 1 .........(ii)

adding (I) and (ii) we get;

2α= 6

α = 3

putting α=3 in eq..(i)

3+ β= 5

β= 2

Now:

αβ= k

3*2=k

k=6

The value of k=6

Answer 2

$\huge\mathfrak\green{Answer:}$

Given:

α and β are the zeroes of the polynomial

f(x)= 1such that α-β=1.

To Find:

We need to find the value of k.

Solution:

Given polynomial is x^2 - 5x + k.

We know that the sum of zeroes that is α + β = -b/a and product of zeroes that is αβ = c/a.

Now, in the given polynomial,

α + β = -b/a = -(-5)/1 = 5

αβ = c/a = k/1 = k

=> α + β = 5______(1)

=> α - β = 1_______(2)

On adding equation 1 and 2 we get,

α + β + α - β = 5 + 1

=> 2α = 6

=> α = 6/2

=> α = 3

Substituting the value of α = 3 in equation 2 we get,

3 - β = 1

=> 3 - 1 = β

=> 2 = β

or β = 2

Now, we know αβ = k.

Substituting the values we have,

3 × 2 = k

6 = k

Therefore the value of k is 6.