GMAT Practice Question: If x^{2}+b x+5=(x+c)^{2} for all numbers x, where b and c...
Question
If x^{2}+b x+5=(x+c)^{2} for all numbers x, where b and c are positive constants, what is the value of b ?
- \sqrt{5}
- \sqrt{10}
- 2 \sqrt{5}
- 2 \sqrt{10}
- 10
Topics: quadratic equations
Solution
Step 1
We expand the right-hand side to compare coefficients.
x^{2}+b x+5 = x^{2} + 2 c x + c^{2}
Step 2
We match the coefficient of x on both sides.
b = 2 c
Step 3
We match the constant term on both sides.
c^{2} = 5
Step 4
Since c is positive, we take the positive square root.
c = \sqrt{5}
Step 5
We substitute c = \sqrt{5} into b = 2 c.
b = 2 \times \sqrt{5}
Answer
2\sqrt{5}
