Question

IF THE ROOTS of the quadratic equation (k -1) x^2 + 2 (k + 1) x-1 =0 are equal then find k and also write the original quadratic equation

Answer 1

Discriminant = $b^2 - 4ac$

                    = [2(k + 1)]² - 4(k - 1)(-1)

                    = [ 4k² + 4 + 8k ] + 4k - 4

                    = 4k² + 4 + 8k + 4k - 4 

                    = 4k² + 12k 


for equal roots, discriminant = 0 
              
                           4k² + 12k   = 0 

                          4k(k + 3)     = 0 

                         

             By Zero product rule,

4k = 0               or         k + 3 =0 

k = 0/4              or         k = - 3 

k =0                  or         k= - 3 

===========================


Taking k =- 3 

Equation =>

(-3-1)x² + 2(-3 + 1)x - 1 =0 
⇒ -4x² -4x - 1 =0 

-----------------------------------
Taking k = 0 

( 0- 1)x² + 2(0 + 1)x - 1= 0 
⇒-x² + 2x - 2 = 0 



 i hope this will help you


(-:

Answer 2

Heya !!!

(K-1)X² + 2(K+1)X - 1 = 0

Here,

A = (K-1) , B = 2(K+1) = 2K +2 and C = -1

Discriminant (D) = B²-4AC

Given that,

Discriminant of the given equation is equal so the discriminant should be equal to 0.

Therefore,

Discriminant = 0

(B²-4AC) = 0

(2K+2)² - 4 × (K-1) × -1 = 0

(2K)² + (2)² + 2 × 2K ×2 - 4 ( -K+1) = 0

4K² + 4 + 4K +8K - 4 = 0

4K² + 12K = 0

4K ( K +3) = 0

4K = 0 OR (K+3) = 0

K = 0/4 OR K = -3




★ Case (1) when K = 0




( 0-1)X² + 2 ( 0+1)X -1 = 0




-X² + 2X -1 = 0




★ Case (2) when K = -3

(K-1)X² + 2(K+1)X -1 = 0

(-3 - 1)X² + 2 ( -3 + 1)X -1 = 0

-4X² -4X -1 = 0

★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★