Question

if alpha and 1/alpha are the zeroes of the polynomial 4x^2+2x+(k-4), find the value of k​

Answer 1

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

Answer 2

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