唔識做功課34

1.
The answer : (B) x² - ax + b = 0

A. false
x² + ax - b = 0, where a and b are positive
The discriminant, Δ = a² - 4b > 0 for a² >4b
There are two real roots.
Factorize x² + ax - b into the form of (x + h)(x - k) whereh and k are positive
Then, (x + h)(x - k) = 0
x = -h or x = k
The two roots have different signs.

B. true
x² - ax + b = 0
The discriminant, Δ = (-a)² - 4b = a² -4b > 0 for a² > 4b
There are two real roots.
Factorize x² - ax + b into the form of (x - h)(x - k) whereh and k are positive
Then, (x - h)(x - k) = 0
x = h or x = k
The two roots have the same sign.

C. false
x² - ax - b = 0, where a and b are positive
The discriminant, Δ = (-a)² - 4(-b) = a² +4b > 0 for a² > 4b
There are two real roots.
Factorize x² - ax - b into the form of (x + h)(x - k) whereh and k are positive
Then, (x + h)(x - k) = 0
x = -h or x = k
The two roots have different signs.


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2.
The answer : (B) 3x² + mx - n = 0

A. false
x² + mx + n = 0, where m and n are positive
The discriminant, Δ = m² - 4n
There is no sufficient information to determine whether Δ is positive ornegative.
The equation may not have real roots.(if Δ is negative)

B. true
3x² + mx - n = 0, where m and n are positive
The discriminant, Δ = m² - 4(3)(-n) = m² +12n > 0 for m and n are positive
There are two real roots.
Factorize 3x² + mx - n into the form of (3x + h)(x - k) or (3x- h)(x + k) where h and k are positive
Then, (3x + h)(x - k) = 0 or (3x - h)(x + k) = 0
(x = -h/3 or x = k) or (x = h/3 or x = -k)
The two roots have different signs.

C. false
-x² + mx - n = 0, where m and n are positive
The discriminant, Δ = m² - 4(-1)(-n) = m² - 4n
There is no sufficient information to determine whether Δ is positive ornegative.
The equation may not have real roots.(if Δ is negative)

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