Answers to first 5 of 15 – Self assessment questions on Quadratic equations: Question 4

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What must be added to the expression 21m2 + 4m to make it a perfect square? Click here to get the question

Solution
21m2 + 4m
Step1
Since the coefficient of m2 is 21, we first divide through by 21 to make the coefficient of m2 to be 1
21m2/21 + 4m/21
= m2 + 4m/21
Step2
Coefficient of m is 4/21
Thus, what must be added is the square of half of the coefficient of m, which is 4/21
Half the coefficient and square it as follows
4/21* 1/2 = 2/21
Square of the halved coefficient is (2/21)2 = 4/441
Thus, 4/441 must be added toto make it a perfect square

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