Question

In copying a second-degree equation, the number without x was written as -30 in¬stead of 30. The answers found were 15 and -2. What are the answers of the correct problem?

Answer 1

ax² + bx - 30 = 0.

x = 15, 225a + 15b - 30 = 0

15a + b = 2 ...... 1

x = -2 4a - 2b - 30 = 0

2a - b = 15 .......2

(1) + (2) \(\rightarrow\) 17a = 17, a = 1

2 x 1 - b = 15 b = -13

Then the equation x² - 13x - 30 = 0

Correct equation is x² - 13x + 30 = 0

\(x=\frac{13\pm\,\sqrt{169-120}}{2},x=\frac{13\,\pm\,7}{2}\)

\(x=\frac{13+7}{2}=10\) or \(\frac{13-7}{2}=3\)

Solutions of the correct problem 10 or 3