Question

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Rewrite x^2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.

a = 4 and b = 3
a = 3 and b = 2
a = 2 and b = 1
a = 1 and b = 4

Answer 1

a = 1 and b = 4

Explanation:

You have:

x^2 − 2x − 3 = 0

(x − a)^2 = b

You need the a and b values:

x^2 − 2x − 3 = 0

a = x^2

b = −2x

c = −3

(x − a)^2 = b

(x - x^2)^2 = −2x

-x^2 (negative times negative equals positive)

−2x^2 (negative times negative equals positive)(cancel x)

(x + x)^2 = 4

x = 1x = 1

(x + 1)^2 = 4

(x − a)^2 = b

(x + 1)^2 = 4

a = 1

b = 4

a = 1 and b = 4

I just took the test.

Answer 2

Answer is option d) a=1 b=4

Explanation:

`given \: equation \: is \: \\ {x}^(2) - 2x - 3 = 0 \\ by \: factorization \: we \: get \\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \\ x = 3 \\ x + 1 = 0 \\ x = - 1 \\ x = 3 \: \: or \: x = - 1 \\ value \: of {(x - a)}^(2) when \: x = 3 \: and \: a = 1 \\ {(3 - 1)}^(2) = {2}^(2) = 4 \\ if \: we \: substitute \: x = - 1 \: we \: get \: same \: answer`

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