Question

If α and β are the zeroes of the polynomial f(x)=x2-6x+k ,find the value of k, such that α 2 + β2=40

Answer 1

Answer :-

The value of k ↠-2

Question :-

• If α and β are the zeroes of the f(x) = x²- 6x + k, find the value of k, such that α² + β² = 40

Given :-

• α² + β² = 40

To find :-

• what is the value of k ?

Solution :-

f(x) = x²- 6x + k --------- (eq - 1 )

α and β are the zeroes of the given polynomial.

Now,

• Sum of zeroes ↠ - b/a

⇒ α + β = -(-6)/1

⇒ α + β = 6

• product of zeroes ↠ c/a

⇒ αβ = k

Since ,

⇒ α² + β² = 40

As we know that

• (α+β)² = α² +β² +2αβ

Now , putting the values , we get

⇒ (6)²↠ 40 + 2k

⇒ 36 ↠40 + 2k

⇒ 36 - 40 ↠2k

⇒ -4 ↠2k

⇒ k ↠-4/2

⇒ k ↠-2

hence , the value of k is -2 .

_____________________

Answer 2

Step-by-step explanation:

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