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

What must be added to the expression 6r2 + 5r to make it a perfect square? Click here to get the question

Solution

6r² + 5r

Step1

Since the coefficient of r² is 6, we first divide through by 6 to make the coefficient of r² to be 1

6r²/6 + ^5r/₆

= r² + ^5r/₆

Step2

Coefficient of r is ⁵/₆

Thus, what must be added is the square of half of the coefficient of r, which is ⁵/₆

Half the coefficient and square it as follows

⁵/₆* ^1/₂ = ⁵/₁₂

Square of the halved coefficient is (⁵/₁₂)² = ²⁵/₁₄₄

Thus, ²⁵/₁₄₄ must be added to to make it a perfect square

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