Question

If a and ß are the zeros of x² - (5 + 7k)x+ 35k, such that a² + ß² = 172 is then the value of k is​

Answer 1

Answer:

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Step-by-step explanation:

x2-5x+k

Here, a=1, b=-5 and c=k  

Now, α+ β = -b/a= -(-5)/1= 5  

α*β  = c/a= k/7= k

Now,α - β =1

Squaring both sides, we get,

(α - β)2=12  

⇒ α2 + β2 - 2αβ = 1

⇒ (α2 + β2 + 2αβ) - 4αβ = 1

⇒ (α +β)2 -4αβ =1

⇒ (5)2-4k=1

⇒ -4k= 7-25

⇒ -4k= -24  

⇒ k=6 So the value of k is 6.

Answer 2

Answer:

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