Question

Write x2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers.
a. (x − 4)2 = 3
b. (x − 3)2 = 2
c. (x − 2)2 = 1
d. (x − 1)2 = 4

Answer 1

x2 -2x-3=0
x2-3x+x-3=0
x(x-3)+1(x-3)=0
therefore x=3 OR x= -1
now, substitute value of x into all four options

Answer 2

Answer:

Option (d) is correct.

Step-by-step explanation:

Given Quadratic equation:

x²-2x-3 = 0

=> (x²-2x+1)-1-3=0

$\implies (x^{2}-2\times x \times 1+1^{2})-4=0$

$\implies (x-1)^{2}=4$

Is in the form of (x-a)²=b ,

where , a = 1 , b = 4

Therefore,

Option (d) is correct.

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