Question:
The coefficient of \(x\) in the equation \(x^2 + px + q = 0\) was taken as 17 in place of 13, and its roots were found to be -2 and -15. The roots of the original equation are:
समीकरण \(x^2 + px + q = 0\) में \(x\) का गुणांक 13 के स्थान पर 17 लिया गया था, और इसके मूल -2 और -15 पाए गए। मूल समीकरण के मूल क्या हैं?
Options:
- 3, 10
- -3, -10
- -5, -18
- None of these
- 3, 10
- -3, -10
- -5, -18
- इनमें से कोई नहीं
Correct Answer: b)
Explanation:
When \(p = 17\) was used, the roots were -2 and -15.
The constant term \(q\) was recorded correctly:
\[q = \text{product of roots} = (-2) \times (-15) = 30\]
The original equation had \(p = 13\) and \(q = 30\):
\[x^2 + 13x + 30 = 0\]
Factoring the quadratic equation:
\[(x + 3)(x + 10) = 0 \implies x = -3, \; -10\]
Hence, the correct option is (b).
गलत गुणांक 17 के साथ मूल -2 और -15 थे।
अचर पद \(q = (-2)(-15) = 30\) सही था।
मूल समीकरण (जहाँ \(p = 13\)):
\[x^2 + 13x + 30 = 0 \implies (x + 3)(x + 10) = 0 \implies x = -3, -10\]
अतः सही विकल्प (b) है।