Name: Jacky Lam
Who is asking: Student
Level: Secondary
Question:
A friend told me that completing square not only can find the vertex but also the roots of a quadratic equation. Is it possible? How? Can you show me how to find the roots of the following equation using completing the square?
8x^{2} + 8x + 4
Hi Jacky,
Completing the square is the way you develop the quadratic formula, so completeing the square will find the roots. Suppose that you want to find the roots of the equation
4x^{2}  12x + 9 = 7
First subtract 7 from both sides of the equation and then divide both sides by 4 so that the coefficient of x^{2} becomes 1.
x^{2}  3x + ^{1}/_{2} = 0
Completion of the square gives
x^{2}  3x + ^{9}/_{4}  ^{9}/_{4} + ^{1}/_{2} = 0
or
(x  ^{3}/_{2})^{2}  ^{7}/_{4} = 0
Thus,
(x  ^{3}/_{2})^{2} = ^{7}/_{4}
and hence
x  ^{3}/_{2} = ^{√7}/_{2} or x  ^{3}/_{2} = ^{√7}/_{2}
Cheers
Penny
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