(x-2-6x+9=(x-3)2), so both zeroes are (3). Recognizing square form is a fast exam method.
Step 2
Why this answer is correct
The correct answer is B. दोनों शून्यक बराबर हैं / Both zeroes are equal. (x-2-6x+9=(x-3)2), so both zeroes are (3). Recognizing square form is a fast exam method.
Step 3
Exam Tip
(x-2-6x+9=(x-3)2) है इसलिए दोनों शून्यक (3) हैं। वर्ग रूप को पहचानना परीक्षा में तेज तरीका है।
(x-4-81=\(x^2-9\)\(x^2+9\)), so the simplified form is \(x^2-9\). In exams, treat \(x^4\) as (\(x^2\)2) while factoring.
Step 2
Why this answer is correct
The correct answer is A. \(,x^2-9,\). (x-4-81=\(x^2-9\)\(x^2+9\)), so the simplified form is \(x^2-9\). In exams, treat \(x^4\) as (\(x^2\)2) while factoring.
Step 3
Exam Tip
(x-4-81=\(x^2-9\)\(x^2+9\)), इसलिए सरल रूप \(x^2-9\) है। परीक्षा में \(x^4\) को (\(x^2\)2) मानकर factor करें।
(x-4-16=\(x^2-4\)\(x^2+4\)), so the simplified form is \(x^2+4\). In exams, treat \(x^4\) as (\(x^2\)2) for factorisation.
Step 2
Why this answer is correct
The correct answer is A. \(,x^2+4,\). (x-4-16=\(x^2-4\)\(x^2+4\)), so the simplified form is \(x^2+4\). In exams, treat \(x^4\) as (\(x^2\)2) for factorisation.
Step 3
Exam Tip
(x-4-16=\(x^2-4\)\(x^2+4\)), इसलिए सरल रूप \(x^2+4\) है। परीक्षा में \(x^4\) को (\(x^2\)2) समझकर factor करें।
Because (x-2-y-2=(x-y)(x+y)), the simplified form is (x+y). In exams, identifying difference of squares is very useful.
Step 2
Why this answer is correct
The correct answer is A. (,x+y,). Because (x-2-y-2=(x-y)(x+y)), the simplified form is (x+y). In exams, identifying difference of squares is very useful.
Step 3
Exam Tip
क्योंकि (x-2-y-2=(x-y)(x+y)), इसलिए सरल रूप (x+y) है। परीक्षा में difference of squares पहचानना बहुत उपयोगी है।
((4x+3)(2x-5)=0), so \(x=-\frac{3}{4}\) and \(\frac{5}{2}\). In exams, change signs while writing roots.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{5}{2},-\frac{3}{4}\). ((4x+3)(2x-5)=0), so \(x=-\frac{3}{4}\) and \(\frac{5}{2}\). In exams, change signs while writing roots.
Step 3
Exam Tip
((4x+3)(2x-5)=0), इसलिए \(x=-\frac{3}{4}\) और \(\frac{5}{2}\) हैं। परीक्षा में संकेत बदलकर मूल लिखें।
((x+5)(8x-3)) does not expand to the given equation, so the options must be checked carefully. The correct factorisation is not present among careless options.
Step 2
Why this answer is correct
The correct answer is C. ((x+5)(8x-3)=0). ((x+5)(8x-3)) does not expand to the given equation, so the options must be checked carefully. The correct factorisation is not present among careless options.
Step 3
Exam Tip
((x+5)(8x-3)=8x-2+37x-15) नहीं बनता; इसलिए विकल्पों में भी सावधानी चाहिए। सही गुणनखंड ((8x+5)(x-3)) नहीं है, अतः यह प्रश्न जाँच आधारित है।
((8x+5)(x-3)=8x-2-19x-15), so it is not for the given equation. In exams, verify each option by expansion.
Step 2
Why this answer is correct
The correct answer is A. ((8x+5)(x-3)=0). ((8x+5)(x-3)=8x-2-19x-15), so it is not for the given equation. In exams, verify each option by expansion.
Step 3
Exam Tip
((8x+5)(x-3)=8x-2-19x-15) नहीं बल्कि यह विस्तार गलत होगा; सही गुणनखंड ((8x+5)(x-3)) से (-24x+5x=-19x) बनता है। परीक्षा में विस्तार से हर विकल्प जांचें।
The equation is equivalent to ((x-p)(x-q)=0), so the roots are (p) and (q). In exams, apply zero product rule to symbolic factors too.
Step 2
Why this answer is correct
The correct answer is A. (x=p,q). The equation is equivalent to ((x-p)(x-q)=0), so the roots are (p) and (q). In exams, apply zero product rule to symbolic factors too.
Step 3
Exam Tip
यह समीकरण ((x-p)(x-q)=0) के बराबर है, इसलिए मूल (p) और (q) हैं। परीक्षा में प्रतीकात्मक गुणनखंडों पर भी शून्य गुणनफल नियम लगाएं।
(12x-2+x-6=(3x-2)(4x+3)), so \(x=\frac{2}{3},-\frac{3}{4}\) is correct. In exams, change signs carefully from factors.
Step 2
Why this answer is correct
The correct answer is A. सही है / Correct. (12x-2+x-6=(3x-2)(4x+3)), so \(x=\frac{2}{3},-\frac{3}{4}\) is correct. In exams, change signs carefully from factors.
Step 3
Exam Tip
(12x-2+x-6=(3x-2)(4x+3)), इसलिए \(x=\frac{2}{3},-\frac{3}{4}\) सही है। परीक्षा में गुणनखंडों से संकेत सावधानी से बदलें।
The first equation has roots \(\frac{5}{2},\frac{8}{5}\), and the second has roots \(\frac{5}{2},\frac{4}{5}\). In exams, solve both equations separately for the common root.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{5}{2}\). The first equation has roots \(\frac{5}{2},\frac{8}{5}\), and the second has roots \(\frac{5}{2},\frac{4}{5}\). In exams, solve both equations separately for the common root.
Step 3
Exam Tip
पहले समीकरण के मूल \(\frac{5}{2},\frac{8}{5}\) और दूसरे के मूल \(\frac{5}{2},\frac{4}{5}\) हैं। परीक्षा में समान मूल के लिए दोनों समीकरण अलग हल करें।
(30x-2-61x+30=(5x-6)(6x-5)), so the roots are \(\frac{6}{5}\) and \(\frac{5}{6}\). In exams, keep the denominators of fractional roots correct.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{6}{5},\frac{5}{6}\). (30x-2-61x+30=(5x-6)(6x-5)), so the roots are \(\frac{6}{5}\) and \(\frac{5}{6}\). In exams, keep the denominators of fractional roots correct.
Step 3
Exam Tip
(30x-2-61x+30=(5x-6)(6x-5)), इसलिए मूल \(\frac{6}{5}\) और \(\frac{5}{6}\) हैं। परीक्षा में भिन्न मूलों के हर को सही रखें।
(18x-2-45x+14=(3x-1)(6x-14)), so the roots are \(\frac{1}{3}\) and \(\frac{7}{3}\). In exams, always check the final factors when a common factor appears.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{1}{3},\frac{7}{3}\). (18x-2-45x+14=(3x-1)(6x-14)), so the roots are \(\frac{1}{3}\) and \(\frac{7}{3}\). In exams, always check the final factors when a common factor appears.
Step 3
Exam Tip
(18x-2-45x+14=(3x-1)(6x-14)), इसलिए मूल \(\frac{1}{3}\) और \(\frac{7}{3}\) हैं। परीक्षा में सामान्य गुणक हो तो अंतिम जाँच जरूर करें।
The equation is equivalent to ((x-s)(x-t)=0), so the roots are (s) and (t). In exams, apply zero product rule to symbolic factors too.
Step 2
Why this answer is correct
The correct answer is A. (x=s,t). The equation is equivalent to ((x-s)(x-t)=0), so the roots are (s) and (t). In exams, apply zero product rule to symbolic factors too.
Step 3
Exam Tip
यह समीकरण ((x-s)(x-t)=0) के बराबर है, इसलिए मूल (s) और (t) हैं। परीक्षा में प्रतीकात्मक गुणनखंडों पर भी शून्य गुणनफल नियम लगाएं।
