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secondary 4 | E Maths
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Date Posted: 4 years ago
Views: 221
x² - 11x + 12
Recall that (a - b)² = a² - 2ab + b²
So if you compare the expressions, you'll realise that 2ab = 11x and we can equate x to a.
So 2ab = 11a and thus b = 11/2
So we can write :
x² - 11x + 12
= x² - 11x + (11/2)² +12 - (11/2)²
= (x - 11/2)² + 12 - 121/4
= (x - 11/2)² - 73/4
= (x - 5½)² - 18¼
so your p = 5½ and q = 18¼
b)
(x - 5½)² - 18¼ = 0
(x - 5½)² = 18¼
x - 5½ = ± √18¼
x = 5½ ± √18¼
Answer is same as what you've gotten
Recall that (a - b)² = a² - 2ab + b²
So if you compare the expressions, you'll realise that 2ab = 11x and we can equate x to a.
So 2ab = 11a and thus b = 11/2
So we can write :
x² - 11x + 12
= x² - 11x + (11/2)² +12 - (11/2)²
= (x - 11/2)² + 12 - 121/4
= (x - 11/2)² - 73/4
= (x - 5½)² - 18¼
so your p = 5½ and q = 18¼
b)
(x - 5½)² - 18¼ = 0
(x - 5½)² = 18¼
x - 5½ = ± √18¼
x = 5½ ± √18¼
Answer is same as what you've gotten
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The trick here is to introduce a term equal to the square of half the coefficient of x.
Here the coefficient of x is -11, so we need to introduce the square of half of this, or the square of (-11/2), or (-11/2)^2.
Of course, we “borrowed” this term to complete the square, so we must “return” it afterwards.
The first three terms which I wrote combine to form a two-term combination inside the bracket, since the three terms a2 + 2ab + b2 combine to form (a + b)^2.
The alternative method is to compare your given expression with the formula a2 + 2ab + b2 and find out what a and b are.
As a side note, your quadratic formula for solving quadratic equations is actually derived from the technique of completing the square.
Here the coefficient of x is -11, so we need to introduce the square of half of this, or the square of (-11/2), or (-11/2)^2.
Of course, we “borrowed” this term to complete the square, so we must “return” it afterwards.
The first three terms which I wrote combine to form a two-term combination inside the bracket, since the three terms a2 + 2ab + b2 combine to form (a + b)^2.
The alternative method is to compare your given expression with the formula a2 + 2ab + b2 and find out what a and b are.
As a side note, your quadratic formula for solving quadratic equations is actually derived from the technique of completing the square.
Date Posted:
4 years ago
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