Question

Find the value of k and the roots if the difference between roots of the equation: X2-5X+k -4=0 is 5.
A) K=1, Roots 0 and 1
B) K=4, Roots 0 and 5
C) K=4, Root 5
D) None of these.

@Akansha what is your favourite Taylor Swift song ^_^

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Answer 1

Answer:

Given that x^2–7x+(k-4) = 0

The roots are

x1 = [7 + (49 -4k+16)^0.5]/2

= [7 + (65–4k)^0.5]/2

x2 = [7 - (49 -4k+16)^0.5]/2

= [7 - (65–4k)^0.5]/2

The difference between x1 and x2 = 5, or

[7 + (65–4k)^0.5]/2 - [7 - (65–4k)^0.5]/2 = 5, or

[7 + (65–4k)^0.5] - [7 - (65–4k)^0.5] = 10, or

7 + (65–4k)^0.5 - 7 + (65–4k)^0.5] = 10, or

2(65–4k)^0.5 = 10, or

(65–4k)^0.5 = 5. Square both sides to get

65–4k = 25, or

4k = 40, or

k = 10.

x1 = [7 + (65–4k)^0.5]/2 = [7 + (65–40)^0.5]/2

= [7 + 25^0.5]/2

= [7+5]/2

= 6

x2 =[7 - (65–4k)^0.5]/2 = [7 - (65–40)^0.5]/2

= [7 - 25^0.5]/2

= [7-5]/2

= 1

Answer. k = 10, x1 = 6 and x2 = 1

Step-by-step explanation:

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btw what is your name

Answer 2

Answer:

A) K=1, Roots 0 and 1 .

Step-by-step explanation:

Hope it helps! :)