Question

Find k for which x square -(k+1)x+4=0 has equal roots.

Answer 1

here equation has equal roots then
D=0
a=-(k+1),b=4,
discriminant=b^2-4ac
b^2-4ac=0 (given d=o)
(4)^2-4×-(k+1)=0
16+4k+4=0
20+4k=0
or k=-5 answer
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Answer 2

Solution :

Compare x² - ( k+1 )x + 4 = 0 with ax²+bx+c=0,

we get

a = 1 , b= - ( k+1 ) , c = 4

Now ,

discriminant ( Δ ) = b² - 4ac = 0 [ given equal roots ]

[ - ( k+ 1 ) ]² - 4 × 1 × 4 = 0

⇒ ( k + 1 )² - 16 = 0

⇒( k + 1 )² = 16

⇒ k + 1 = √16 or - √16

k + 1 = 4 or k + 1 = -4

k = 4 -1 or k = -4 -1

k = 3 or k = -5

....