If sum of squares zeroes of polynomial f(x)=x2-8x+k is 40.Find k
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Step-by-step explanation:
may be 30 is the correct answer
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Answer:
Value of k is 24.
Step-by-step explanation:
Given :
Sum of squares of zeroes of the polynomial f(x) = x² - 8x + k is 40
Let α, β be the zeroes the given polynomial
So, Sum of squares of zeroes = α² + β² = 40
Comparing the given polynomial with ax² + bx + c we get
a = 1
b = - 8
c = k
Sum of zeroes = α + β = - b/a = - ( - 8 ) / 1 = 8
Product of zeroes = αβ = c/a = k/1 = k
We know that
( α + β )² = α² + β² + 2αβ
Substituting the known values
( 8 )² = 40 + k
64 = 40 + k
k = 64 - 40
k = 24
Therefore the value of k is 24.
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