If the sum of the squares zeros of the quadratic polynomial f(x)=x^2-8x+k. Find k

ankarskogC

ankarskogC

Answered question

2021-09-06

If the sum of the squares zeros of the quadratic polynomial f(x)=x28x+k. Find k.

Answer & Explanation

Laith Petty

Laith Petty

Skilled2021-09-07Added 103 answers

Consider the quadratic polynomials,
f(x)=x28x+k
Comparing the given quadratic polynomias with standart polynomials
f(x)=ax2+bx+c
After comparing,
a=1, b=8 and c=k
Let the zeros of the polynomials is α and β
According to the question,
sum of the square of the quadratic Polynomials
α2+β2=40
Sum of zeros of the polynomials is,
α+β=ba
α+β=81
α+β=8
The product of the standard quadratic polynomials,
αβ=ca
αβ=k1
αβ=k
To calculate the value of "k"
From equation
α2+β2=40
(α+β)22αβ=40
(8)22k=40
642k=40
2k=6440
2k=24
k=12
Hence the value of k is 12.

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