if alpha and 1/alpha are the zeroes of the polynomial 4x^2+2x+(k-4), find the value of k About the author Skylar
Question if alpha and 1/alpha are the zeroes of the polynomial 4x^2+2x+(k-4), find the value of k Answer → α × β = c/a → α ×1/α = (k-4)/4 → 1 × 4 = (k-4) → 4 = k-4 → 4+4 = k → k = 8 Reply
Step-by-step explanation: Given:– α and 1/α are the zeroes of the polynomial 4x^2+2x+(k-4) To find:– Find the value of k ? Solution:– Given that Given Quardratic polynomial p(x) = 4x^2+2x+(k-4) On Comparing this with the standard quadratic Polynomial ax^2+bx+c then a = 4 b=2 c=k-4 Given zeroes are α and 1/α We Know that Sum of the zeroes = -b/a α +( 1/α) = -2/4 α + (1/α) = -1/2————(1) Product of the zeroes = c/a =>( α )(1/α) = (k-4)/2 => 1 = (k-4)/2 => 2=k-4 => k-4 = 2 => k = 2+4 => k =6 Therefore,k = 6 Answer:– The value of k for the given problem is 6 Used formulae:– 1.The standard quadratic Polynomial ax^2+bx+c 2.Sum of the zeroes = -b/a 3.Product of the zeroes = c/a Reply
Question
Answer
→ α × β = c/a
→ α ×1/α = (k-4)/4
→ 1 × 4 = (k-4)
→ 4 = k-4
→ 4+4 = k
→ k = 8
Step-by-step explanation:
Given:–
α and 1/α are the zeroes of the polynomial 4x^2+2x+(k-4)
To find:–
Find the value of k ?
Solution:–
Given that
Given Quardratic polynomial p(x) = 4x^2+2x+(k-4)
On Comparing this with the standard quadratic Polynomial ax^2+bx+c then
a = 4
b=2
c=k-4
Given zeroes are α and 1/α
We Know that
Sum of the zeroes = -b/a
α +( 1/α) = -2/4
α + (1/α) = -1/2————(1)
Product of the zeroes = c/a
=>( α )(1/α) = (k-4)/2
=> 1 = (k-4)/2
=> 2=k-4
=> k-4 = 2
=> k = 2+4
=> k =6
Therefore,k = 6
Answer:–
The value of k for the given problem is 6
Used formulae:–
1.The standard quadratic Polynomial ax^2+bx+c
2.Sum of the zeroes = -b/a
3.Product of the zeroes = c/a