Question

if alpha and beta are the zeros of polynomial x^2 + 5x + k and 2alpha +5beta =-1 find the values of k. ​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

k = -24

Step-by-step explanation:

Given :

• α and β are the zeroes of the polynomial x² + 5x + k
• 2α + 5β = -1

To find :

the value of k

Solution :

To solve this question,we must know the relation between zeros and coefficients of the quadratic polynomial.

Sum of zeros = -(x coefficient)/x² coefficient

Product of zeros = constant term/x² coefficient

For the given quadratic polynomial,

constant term = k

x coefficient = 5

x² coefficient = 1

Therefore, α + β = -5/1 = -5

Also,

2α + 5β = -1

2α + 2β + 3β = -1

2(α + β) + 3β = -1

2(-5) + 3β = -1

-10 + 3β = -1

3β = 10 - 1

3β = 9

β = 9/3 = 3

Substitute the value of β,

α + β = -5

α + 3 = -5

α = - 5 - 3 = -8

From the relation between product of zeros and coefficients :

αβ = k

(-8)(3) = k

k = -24

Therefore, the value of k is -24