Question

if alfa and bita are the zeroes of the polynomial y sq.-ky + 4 (k is a positive integer) such that alfa-bita=3, then what is the value of k?​

Answer 1

Answer:-

Given:

α , β are the zeroes of y² - ky + 4 = 0.

On comparing with standard form of a Quadratic equation i.e., ax² + bx + c = 0 ;

Let ,

• a = 1
• b = - k
• c = 4

We know that,

Sum of the zeroes = - b/a

⟹ α + β = - ( - k/1)

⟹ α + β = k -- equation (1)

Product of the zeroes = c/a

⟹ αβ = 4 -- equation (2)

Also given that,

⟹ α - β = 3 -- equation (3)

We know that,

• (a + b)² = (a - b)² + 4ab

So,

⟹ (α + β)² = (α - β)² + 4αβ

Substitute the values from equations (1) , (2) & (3).

⟹ k² = (3)² + 4(4)

⟹ k² = 9 + 16

⟹ k² = 25

⟹ k = √25

⟹ k = ± 5

In the question it is given that k is a positive integer. so ( - 5) is neglected.

∴ The value of k is 5.

Answer 2

${\huge{\underbrace{\rm{Answer\checkmark}}}}$

★ Given -

• y² - ky + 4 = 0 .

• $\alpha$ and $\beta$ are the roots of the above equation .

• $\alpha - \beta$ = 3

★ To Find -

• The value of ‘k’ = ?

★ Solution -

Refer to tha attachment

${\boxed{\rm{K=5}}}$