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## If a, ß are zeroes of P(x) = x² – 6x + k, such that a² + ² = 20 then find the value of k.

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If a, ß are zeroes of P(x) = x² – 6x + k, such that a² + ² = 20 then find the value of k.

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Mathematics
2 months
2021-07-27T14:31:38+00:00
2021-07-27T14:31:38+00:00 1 Answers
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## Answers ( )

We have,

f(x) = x2 – 6x + k

α² + β² = 20

➝ ( α + β )² – 2αβ = 20 ——(1)

α + β = -b/a

➝ -(-6)/1

➝

6αβ = c/a

➝ k/1

➝

kPutting Value in (1),( α + β )² – 2αβ = 20

➝ ( 6 )² – 2k = 20

➝ 36 – 2k = 20

➝ – 2k = 20 – 36

➝ – 2k = -16

➝ k = -16/-2

➝

k = 8The value of kis8.