Question

if alpha and beta are zeros of polynomial f(x)=kx2+7x+7 such that alpha2+beta2=42 find k​

Answer 1

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Answer 2

Answer:

Value of k is 1 or - 49/42

Step-by-step explanation:

Given :

α, β are zeroes of the polynomial f(x) = kx² + 7x + 7

α² + β² = 42

Comparing the given polynomial with ax² + bx + c we get

a = k

b = 7

c = 7

Sum of zeroes = α + β = - b/a = - 7/k

Product of zeroes = αβ = c/a = 7/k

We know that

( α + β )² = α² + β² + 2αβ

Substituting the known values

( - 7/k )² = 42 + 7/k

49/k² = 42 + 7/k

49/k² - 7/k = 42

( 49 - 7k ) / k² = 42

49 - 7k = 42k²

42k² + 7k - 49 = 0

42k² + 49k - 42k - 49 = 0

k( 42k + 49 ) - 1( 42k + 49 ) = 0

( k - 1 )( 42k + 49 ) = 0

k - 1 = 0 OR 42k + 49 = 0

k = 1 OR k = - 49/42

Therefore the value of k is 1 or - 49/42