Question

If a a and b are the zeros of the polynomial f(x) = x^2 - 5x+ k such that a - B = 1 , find the value of k​

Answer 1

Answer:

Hey Mate,

Given Question :If a and b are the zeros of the polynomial f(x) = x^2 - 5x+ k such that a - B = 1 , find the value of k​.

Step-by-step explanation:

solution :

→ f (x)  = x² - 5 x + k

→ a = 1 ,

→ b = -5

→ c = k

→ a + B = -b / a                                                           a . B = c /a

→ - ( -5)  / 1                                                                         k/1  = k

→ 5

→ ∵ a  - B  = 1

→ ( a -B )² = ( 1 )²

→ (a - B)²  = (a + B) ² -  4 a B

→ ( 1 ) ² = ( 5 ) ² -  4 × k

→ 1 = 25 - 4k

→ 1 - 25 = -4k

→ - 24  = -4k   ( ∵ - and - gets cancelled)

→ 24 / 4   = k

→ 6 = k  is the value

thank you

Answer 2

Step-by-step explanation:

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K=6

Since a and b are the zeros of the polynomial f(x)=x2−5x+k

The standard quadratic equation is px2+qx+r=0 

Then Sum of roots = −pq 

and Product of roots = pr

Therefore,

a+b=5 and ab=k

Now, a−b=1

(a−b)2=1

(a+b)2−4ab=1

25−4k=1

24=4k

k=6