Question

If one root of the equation (k – 1)x2 – 10x + 3 = 0 is the reciprocal of the other, then
then the value a
​

Answer 1

Step-by-step explanation:

hope it helps you ☺️

Answer 2

Answer:

k = 4

Step-by-step explanation:

Let say One root is

P then other root is 1/P

Products of roots = c/a

=> P * (1/P) = c/a

=> 1 = c/a

=> c = a

=> k - 1 = 3

=> k = 4

(4-1)x² - 10x + 3 = 0

=> 3x² - 9x - x + 3 = 0

=> 3x(x - 3) - 1(x - 3) = 0

=>(3x - 1)(x - 3) = 0

=> x = 1/3 , 3

Another method

roots P & 1/P

(x -  P)(x - 1/P) = 0

=> x² - x(P + 1/P)  + 1 = 0

multiplying by 3

=> 3x² - 3x(P + 1/P) + 3 = 0

Equating with

(k-1)x² - 10x + 3 = 0

=> k - 1 = 3 => k = 4

3(P + 1/P) = 10

=> 3P² - 10P + 3 = 0

=> (3P - 1)(P -3) = 0

P = 1/3 , 3

i hope this helped you

thankyou and have a great weekend