75 results found for "equal-roots" in Class 10.
Question
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(5x^2-4x+t=0\) के वास्तविक और समान मूलों के लिए (t) क्या होगा?
What is (t) for real and equal roots of \(5x^2-4x+t=0\)?
#quadratic equations
#parameter
#equal roots
#fraction
A \(\frac{4}{5}\)
B \(\frac{5}{4}\)
C (4)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(\frac{4}{5}\)
Step 1
Concept
(D=(-4)2 -4(5)t=0) gives \(t=\frac{4}{5}\). Always set (D=0) for equal roots.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4}{5}\). (D=(-4)2 -4(5)t=0) gives \(t=\frac{4}{5}\). Always set (D=0) for equal roots.
Step 3
Exam Tip
(D=(-4)2 -4(5)t=0) से \(t=\frac{4}{5}\) मिलता है। समान मूलों के लिए हमेशा (D=0) रखें।
Login to save your score, XP, coins and progress.
Question
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
किस समीकरण के दो वास्तविक और समान मूल होंगे?
Which equation will have two real and equal roots?
#quadratic equations
#choose equation
#equal roots
A \(x^2+10x+25=0\)
B \(x^2+10x+24=0\)
C \(x^2+10x+30=0\)
D \(2x^2+10x+25=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+10x+25=0\)
Step 1
Concept
In the first equation, (D=102 -4(1)(25)=0). A perfect square form often gives equal roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+10x+25=0\). In the first equation, (D=102 -4(1)(25)=0). A perfect square form often gives equal roots.
Step 3
Exam Tip
पहले समीकरण में (D=102 -4(1)(25)=0) है। पूर्ण वर्ग रूप अक्सर समान मूल देता है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
(x-2 -2(k+7)x+k-2 =0) के समान मूलों के लिए (k) क्या होगा?
What is (k) for equal roots of (x-2 -2(k+7)x+k-2 =0)?
#quadratic
#discriminant
#parameter
A \(k=-\frac{7}{2}\)
B \(k=\frac{7}{2}\)
C (k=-7)
D (k=7)
Explanation opens after your attempt
Correct Answer
A. \(k=-\frac{7}{2}\)
Step 1
Concept
(D=4(k+7)2 -4k-2 =0) gives ((k+7)2 =k-2 ), so (14k+49=0) and \(k=-\frac{7}{2}\). In exams, expand squares carefully.
Step 2
Why this answer is correct
The correct answer is A. \(k=-\frac{7}{2}\). (D=4(k+7)2 -4k-2 =0) gives ((k+7)2 =k-2 ), so (14k+49=0) and \(k=-\frac{7}{2}\). In exams, expand squares carefully.
Step 3
Exam Tip
(D=4(k+7)2 -4k-2 =0) से ((k+7)2 =k-2 ), इसलिए (14k+49=0) और \(k=-\frac{7}{2}\) है। परीक्षा में वर्ग फैलाते समय सावधानी रखें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(kx^2-26x+169=0\) के समान मूल हैं, तो (k) क्या होगा?
If \(kx^2-26x+169=0\) has equal roots, what is (k)?
#quadratic
#discriminant
#parameter
A (1)
B (2)
C (13)
D (169)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (676-676k=0) and (k=1). In exams, keep (a=k) correctly.
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots, (D=0), so (676-676k=0) and (k=1). In exams, keep (a=k) correctly.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (676-676k=0) और (k=1) है। परीक्षा में (a=k) को ठीक से रखें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2-24x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-24x+m=0\) has real and equal roots, what is the value of (m)?
#quadratic
#discriminant
#equal-roots
A (m=144)
B (m=24)
C (m=48)
D (m=576)
Explanation opens after your attempt
Correct Answer
A. (m=144)
Step 1
Concept
For real and equal roots, (D=0), so (576-4m=0) gives (m=144). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=144). For real and equal roots, (D=0), so (576-4m=0) gives (m=144). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (576-4m=0) से (m=144) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि (x-2 -2(k-5)x+k-2 -36=0) के मूल समान हों, तो (k) का मान क्या होगा?
If (x-2 -2(k-5)x+k-2 -36=0) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A \(k=\frac{61}{10}\)
B \(k=-\frac{61}{10}\)
C (k=5)
D (k=36)
Explanation opens after your attempt
Correct Answer
A. \(k=\frac{61}{10}\)
Step 1
Concept
For equal roots, (D=0), so ((k-5)2 =k-2 -36) and \(k=\frac{61}{10}\). In exams, handle constant terms carefully while expanding squares.
Step 2
Why this answer is correct
The correct answer is A. \(k=\frac{61}{10}\). For equal roots, (D=0), so ((k-5)2 =k-2 -36) and \(k=\frac{61}{10}\). In exams, handle constant terms carefully while expanding squares.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((k-5)2 =k-2 -36) और \(k=\frac{61}{10}\) है। परीक्षा में वर्ग फैलाते समय स्थिर पद ध्यान से लें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
(x-2 -2(k+6)x+k-2 =0) के समान मूलों के लिए (k) क्या होगा?
What is (k) for equal roots of (x-2 -2(k+6)x+k-2 =0)?
#quadratic
#discriminant
#parameter
A (k=-3)
B (k=3)
C (k=-6)
D (k=6)
Explanation opens after your attempt
Step 1
Concept
(D=4(k+6)2 -4k-2 =0) gives ((k+6)2 =k-2 ), so (12k+36=0) and (k=-3). In exams, expand squares carefully.
Step 2
Why this answer is correct
The correct answer is A. (k=-3). (D=4(k+6)2 -4k-2 =0) gives ((k+6)2 =k-2 ), so (12k+36=0) and (k=-3). In exams, expand squares carefully.
Step 3
Exam Tip
(D=4(k+6)2 -4k-2 =0) से ((k+6)2 =k-2 ), इसलिए (12k+36=0) और (k=-3) है। परीक्षा में वर्ग फैलाते समय सावधानी रखें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(kx^2-22x+121=0\) के समान मूल हैं, तो (k) क्या होगा?
If \(kx^2-22x+121=0\) has equal roots, what is (k)?
#quadratic
#discriminant
#parameter
A (1)
B (2)
C (11)
D (121)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (484-484k=0) and (k=1). In exams, keep (a=k) correctly.
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots, (D=0), so (484-484k=0) and (k=1). In exams, keep (a=k) correctly.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (484-484k=0) और (k=1) है। परीक्षा में (a=k) को ठीक से रखें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2-22x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-22x+m=0\) has real and equal roots, what is the value of (m)?
#quadratic
#discriminant
#equal-roots
A (m=121)
B (m=22)
C (m=44)
D (m=484)
Explanation opens after your attempt
Correct Answer
A. (m=121)
Step 1
Concept
For real and equal roots, (D=0), so (484-4m=0) gives (m=121). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=121). For real and equal roots, (D=0), so (484-4m=0) gives (m=121). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (484-4m=0) से (m=121) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि (x-2 -2(k-4)x+k-2 -25=0) के मूल समान हों, तो (k) का मान क्या होगा?
If (x-2 -2(k-4)x+k-2 -25=0) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A \(k=\frac{41}{8}\)
B \(k=-\frac{41}{8}\)
C (k=4)
D (k=25)
Explanation opens after your attempt
Correct Answer
A. \(k=\frac{41}{8}\)
Step 1
Concept
For equal roots, (D=0), so ((k-4)2 =k-2 -25) and \(k=\frac{41}{8}\). In exams, handle constant terms carefully while expanding squares.
Step 2
Why this answer is correct
The correct answer is A. \(k=\frac{41}{8}\). For equal roots, (D=0), so ((k-4)2 =k-2 -25) and \(k=\frac{41}{8}\). In exams, handle constant terms carefully while expanding squares.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((k-4)2 =k-2 -25) और \(k=\frac{41}{8}\) है। परीक्षा में वर्ग फैलाते समय स्थिर पद ध्यान से लें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
(x-2 -2(k+5)x+k-2 =0) के समान मूलों के लिए (k) क्या होगा?
What is (k) for equal roots of (x-2 -2(k+5)x+k-2 =0)?
#quadratic
#discriminant
#parameter
A \(k=-\frac{5}{2}\)
B \(k=\frac{5}{2}\)
C (k=-5)
D (k=5)
Explanation opens after your attempt
Correct Answer
A. \(k=-\frac{5}{2}\)
Step 1
Concept
(D=4(k+5)2 -4k-2 =0) gives ((k+5)2 =k-2 ), so (10k+25=0) and \(k=-\frac{5}{2}\). In exams, expand squares carefully.
Step 2
Why this answer is correct
The correct answer is A. \(k=-\frac{5}{2}\). (D=4(k+5)2 -4k-2 =0) gives ((k+5)2 =k-2 ), so (10k+25=0) and \(k=-\frac{5}{2}\). In exams, expand squares carefully.
Step 3
Exam Tip
(D=4(k+5)2 -4k-2 =0) से ((k+5)2 =k-2 ), इसलिए (10k+25=0) और \(k=-\frac{5}{2}\) है। परीक्षा में वर्ग फैलाते समय सावधानी रखें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(kx^2-18x+81=0\) के समान मूल हैं, तो (k) क्या होगा?
If \(kx^2-18x+81=0\) has equal roots, what is (k)?
#quadratic
#discriminant
#parameter
A (1)
B (2)
C (9)
D (81)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (324-324k=0) and (k=1). In exams, keep (a=k) correctly.
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots, (D=0), so (324-324k=0) and (k=1). In exams, keep (a=k) correctly.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (324-324k=0) और (k=1) है। परीक्षा में (a=k) को ठीक से रखें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2-20x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-20x+m=0\) has real and equal roots, what is the value of (m)?
#quadratic
#discriminant
#equal-roots
A (m=100)
B (m=20)
C (m=40)
D (m=400)
Explanation opens after your attempt
Correct Answer
A. (m=100)
Step 1
Concept
For real and equal roots, (D=0), so (400-4m=0) gives (m=100). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=100). For real and equal roots, (D=0), so (400-4m=0) gives (m=100). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (400-4m=0) से (m=100) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि (x-2 -2(k+3)x+k-2 -16=0) के समान मूलों के लिए सही (k) चाहिए, तो कौनसा मान सही है?
If the correct (k) is needed for equal roots of (x-2 -2(k+3)x+k-2 -16=0), which value is correct?
#quadratic
#discriminant
#correction
A \(k=\frac{7}{6}\)
B \(k=-\frac{25}{6}\)
C \(k=\frac{25}{6}\)
D \(k=-\frac{7}{6}\)
Explanation opens after your attempt
Correct Answer
B. \(k=-\frac{25}{6}\)
Step 1
Concept
(D=4(k+3)2 -4\(k^2-16\)=0) gives ((k+3)2 =k-2 -16), so (6k+25=0) and \(k=-\frac{25}{6}\). In exams, handle the constant term carefully after expansion.
Step 2
Why this answer is correct
The correct answer is B. \(k=-\frac{25}{6}\). (D=4(k+3)2 -4\(k^2-16\)=0) gives ((k+3)2 =k-2 -16), so (6k+25=0) and \(k=-\frac{25}{6}\). In exams, handle the constant term carefully after expansion.
Step 3
Exam Tip
(D=4(k+3)2 -4\(k^2-16\)=0) से ((k+3)2 =k-2 -16), इसलिए (6k+25=0) और \(k=-\frac{25}{6}\) है। परीक्षा में विस्तार के बाद स्थिर पद ध्यान से जोड़ें।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि (x-2 -2(k+3)x+k-2 -16=0) के मूल समान हों, तो (k) का मान क्या होगा?
If (x-2 -2(k+3)x+k-2 -16=0) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A \(k=\frac{7}{6}\)
B \(k=-\frac{7}{6}\)
C (k=3)
D (k=16)
Explanation opens after your attempt
Correct Answer
A. \(k=\frac{7}{6}\)
Step 1
Concept
For equal roots, (D=0), so (4(k+3)2 -4\(k^2-16\)=0) must be expanded carefully; a wrong expansion changes the answer. In exams, recheck parameter expansion.
Step 2
Why this answer is correct
The correct answer is A. \(k=\frac{7}{6}\). For equal roots, (D=0), so (4(k+3)2 -4\(k^2-16\)=0) must be expanded carefully; a wrong expansion changes the answer. In exams, recheck parameter expansion.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (4(k+3)2 -4\(k^2-16\)=0) से (6k+25=0) नहीं बल्कि (6k+25) गलत होगा; सही फैलाने पर (6k+25) नहीं बनता। परीक्षा में विस्तार दोबारा जांचें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
(x-2 -2(k+4)x+k-2 =0) के समान मूलों के लिए (k) क्या होगा?
What is (k) for equal roots of (x-2 -2(k+4)x+k-2 =0)?
#quadratic
#discriminant
#parameter
A (k=-2)
B (k=2)
C (k=-4)
D (k=4)
Explanation opens after your attempt
Step 1
Concept
(D=4(k+4)2 -4k-2 =0) gives ((k+4)2 =k-2 ), so (8k+16=0) and (k=-2). In exams, expand squares carefully.
Step 2
Why this answer is correct
The correct answer is A. (k=-2). (D=4(k+4)2 -4k-2 =0) gives ((k+4)2 =k-2 ), so (8k+16=0) and (k=-2). In exams, expand squares carefully.
Step 3
Exam Tip
(D=4(k+4)2 -4k-2 =0) से ((k+4)2 =k-2 ), इसलिए (8k+16=0) और (k=-2) है। परीक्षा में वर्ग फैलाते समय सावधानी रखें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(kx^2-14x+49=0\) के समान मूल हैं, तो (k) क्या होगा?
If \(kx^2-14x+49=0\) has equal roots, what is (k)?
#quadratic
#discriminant
#parameter
A (1)
B (2)
C (7)
D (49)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (196-196k=0) and (k=1). In exams, keep (a=k) correctly.
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots, (D=0), so (196-196k=0) and (k=1). In exams, keep (a=k) correctly.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (196-196k=0) और (k=1) है। परीक्षा में (a=k) को ठीक से रखें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2-18x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-18x+m=0\) has real and equal roots, what is the value of (m)?
#quadratic
#discriminant
#equal-roots
A (m=81)
B (m=18)
C (m=36)
D (m=324)
Explanation opens after your attempt
Step 1
Concept
For real and equal roots, (D=0), so (324-4m=0) gives (m=81). In exams, equal roots mean (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=81). For real and equal roots, (D=0), so (324-4m=0) gives (m=81). In exams, equal roots mean (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (324-4m=0) से (m=81) है। परीक्षा में समान मूल का मतलब (D=0) होता है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि (x-2 -2(k-2)x+k-2 -9=0) के मूल समान हों, तो (k) का मान क्या होगा?
If (x-2 -2(k-2)x+k-2 -9=0) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A \(k=\frac{13}{4}\)
B \(k=-\frac{13}{4}\)
C (k=2)
D (k=9)
Explanation opens after your attempt
Correct Answer
A. \(k=\frac{13}{4}\)
Step 1
Concept
For equal roots, (D=0), so (4(k-2)2 -4\(k^2-9\)=0) gives (-4k+13=0). In exams, expand (D) carefully in parameter questions.
Step 2
Why this answer is correct
The correct answer is A. \(k=\frac{13}{4}\). For equal roots, (D=0), so (4(k-2)2 -4\(k^2-9\)=0) gives (-4k+13=0). In exams, expand (D) carefully in parameter questions.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (4(k-2)2 -4\(k^2-9\)=0) से (-4k+13=0) मिलता है। परीक्षा में पैरामीटर वाले प्रश्नों में (D) सावधानी से फैलाएं।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
(x-2 -2(k+3)x+k-2 =0) के समान मूलों के लिए (k) क्या होगा?
What is (k) for equal roots of (x-2 -2(k+3)x+k-2 =0)?
#quadratic
#discriminant
#parameter
A \(k=-\frac{3}{2}\)
B \(k=\frac{3}{2}\)
C (k=-3)
D (k=3)
Explanation opens after your attempt
Correct Answer
A. \(k=-\frac{3}{2}\)
Step 1
Concept
(D=4(k+3)2 -4k-2 =0) gives ((k+3)2 =k-2 ), so (6k+9=0) and \(k=-\frac{3}{2}\). In exams, expand squares carefully.
Step 2
Why this answer is correct
The correct answer is A. \(k=-\frac{3}{2}\). (D=4(k+3)2 -4k-2 =0) gives ((k+3)2 =k-2 ), so (6k+9=0) and \(k=-\frac{3}{2}\). In exams, expand squares carefully.
Step 3
Exam Tip
(D=4(k+3)2 -4k-2 =0) से ((k+3)2 =k-2 ), इसलिए (6k+9=0) और \(k=-\frac{3}{2}\) है। परीक्षा में वर्ग फैलाते समय सावधानी रखें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(kx^2-10x+25=0\) के समान मूल हैं, तो (k) क्या होगा?
If \(kx^2-10x+25=0\) has equal roots, what is (k)?
#quadratic
#discriminant
#parameter
A (1)
B (2)
C (5)
D (25)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (100-100k=0) and (k=1). In exams, keep (a=k) correctly.
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots, (D=0), so (100-100k=0) and (k=1). In exams, keep (a=k) correctly.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (100-100k=0) और (k=1) है। परीक्षा में (a=k) को ठीक से रखें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2-14x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-14x+m=0\) has real and equal roots, what is the value of (m)?
#quadratic
#discriminant
#equal-roots
A (m=49)
B (m=14)
C (m=28)
D (m=196)
Explanation opens after your attempt
Step 1
Concept
For real and equal roots, (D=0), so (196-4m=0) gives (m=49). In exams, equal roots mean (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=49). For real and equal roots, (D=0), so (196-4m=0) gives (m=49). In exams, equal roots mean (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (196-4m=0) से (m=49) है। परीक्षा में समान मूल का मतलब (D=0) होता है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि (x-2 -2(k-1)x+k-2 -4=0) के मूल समान हों, तो (k) का मान क्या होगा?
If (x-2 -2(k-1)x+k-2 -4=0) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A \(k=\frac{5}{2}\)
B \(k=-\frac{5}{2}\)
C (k=2)
D (k=1)
Explanation opens after your attempt
Correct Answer
A. \(k=\frac{5}{2}\)
Step 1
Concept
For equal roots, (D=0), so (4(k-1)2 -4\(k^2-4\)=0) gives (-2k+5=0). In exams, expand (D) carefully in parameter questions.
Step 2
Why this answer is correct
The correct answer is A. \(k=\frac{5}{2}\). For equal roots, (D=0), so (4(k-1)2 -4\(k^2-4\)=0) gives (-2k+5=0). In exams, expand (D) carefully in parameter questions.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (4(k-1)2 -4\(k^2-4\)=0) से (-2k+5=0) मिलता है। परीक्षा में पैरामीटर वाले प्रश्नों में (D) को सावधानी से फैलाएं।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
(x-2 -2(k+2)x+k-2 =0) के समान मूलों के लिए (k) क्या होगा?
What is (k) for equal roots of (x-2 -2(k+2)x+k-2 =0)?
#quadratic
#discriminant
#parameter
A (k=-1)
B (k=1)
C (k=-2)
D (k=2)
Explanation opens after your attempt
Step 1
Concept
(D=4(k+2)2 -4k-2 =0) gives ((k+2)2 =k-2 ), so (4k+4=0) and (k=-1). In exams, expand squares carefully.
Step 2
Why this answer is correct
The correct answer is A. (k=-1). (D=4(k+2)2 -4k-2 =0) gives ((k+2)2 =k-2 ), so (4k+4=0) and (k=-1). In exams, expand squares carefully.
Step 3
Exam Tip
(D=4(k+2)2 -4k-2 =0) से ((k+2)2 =k-2 ), इसलिए (4k+4=0) और (k=-1) है। परीक्षा में वर्ग फैलाते समय सावधानी रखें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(kx^2-6x+9=0\) के समान मूल हैं, तो (k) क्या होगा?
If \(kx^2-6x+9=0\) has equal roots, what is (k)?
#quadratic
#discriminant
#parameter
A (1)
B (2)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (36-36k=0) and (k=1). In exams, keep (a=k) correctly.
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots, (D=0), so (36-36k=0) and (k=1). In exams, keep (a=k) correctly.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (36-36k=0) और (k=1) है। परीक्षा में (a=k) को ठीक से रखें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2-6x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-6x+m=0\) has real and equal roots, what is the value of (m)?
#quadratic
#discriminant
#equal-roots
A (m=9)
B (m=6)
C (m=12)
D (m=36)
Explanation opens after your attempt
Step 1
Concept
For real and equal roots, (D=0), so (36-4m=0) gives (m=9). In exams, remember equal roots mean (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=9). For real and equal roots, (D=0), so (36-4m=0) gives (m=9). In exams, remember equal roots mean (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (36-4m=0) से (m=9) है। परीक्षा में समान मूल का मतलब (D=0) याद रखें।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि (x-2 -2(k+1)x+k-2 =0) के मूल समान हों, तो (k) का मान क्या होगा?
If (x-2 -2(k+1)x+k-2 =0) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A \(k=-\frac{1}{2}\)
B \(k=\frac{1}{2}\)
C (k=-1)
D (k=1)
Explanation opens after your attempt
Correct Answer
A. \(k=-\frac{1}{2}\)
Step 1
Concept
For equal roots, (D=0), so (4(k+1)2 -4k-2 =0) gives (2k+1=0). In exams, write (D) first in parameter questions.
Step 2
Why this answer is correct
The correct answer is A. \(k=-\frac{1}{2}\). For equal roots, (D=0), so (4(k+1)2 -4k-2 =0) gives (2k+1=0). In exams, write (D) first in parameter questions.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (4(k+1)2 -4k-2 =0) से (2k+1=0) मिलता है। परीक्षा में पैरामीटर वाले प्रश्नों में पहले (D) लिखें।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2-2kx+25=0\) के समान मूल हों और (k>0), तो (k) का मान क्या होगा?
If \(x^2-2kx+25=0\) has equal roots and (k>0), what is the value of (k)?
#quadratic
#discriminant
#parameter
A (5)
B (-5)
C (10)
D (25)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so ((-2k)2 -4(1)(25)=0) gives (k=5). In exams, apply the condition (k>0).
Step 2
Why this answer is correct
The correct answer is A. (5). For equal roots, (D=0), so ((-2k)2 -4(1)(25)=0) gives (k=5). In exams, apply the condition (k>0).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((-2k)2 -4(1)(25)=0) से (k=5) मिलता है। परीक्षा में (k>0) वाली शर्त जरूर लगाएं।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि (D=0) और (a=4,b=-16), तो समान मूल क्या होगा?
If (D=0) and (a=4,b=-16), what will be the equal root?
#quadratic
#equal-roots
#formula
A (x=2)
B (x=-2)
C (x=4)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{16}{8}=2\). In exams, this short formula is useful when (D=0).
Step 2
Why this answer is correct
The correct answer is A. (x=2). The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{16}{8}=2\). In exams, this short formula is useful when (D=0).
Step 3
Exam Tip
समान मूल \(x=\frac{-b}{2a}\) होता है, इसलिए \(x=\frac{16}{8}=2\) है। परीक्षा में (D=0) पर यह छोटा सूत्र उपयोगी है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2+kx+36=0\) के समान मूल हैं और (k>0), तो (k) क्या होगा?
If \(x^2+kx+36=0\) has equal roots and (k>0), what is (k)?
#quadratic
#discriminant
#parameter
A (12)
B (-12)
C (6)
D (36)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(k^2-144=0\), so \(k=\pm12\), and (k>0) gives (k=12). In exams, apply the given condition.
Step 2
Why this answer is correct
The correct answer is A. (12). For equal roots, \(k^2-144=0\), so \(k=\pm12\), and (k>0) gives (k=12). In exams, apply the given condition.
Step 3
Exam Tip
समान मूलों के लिए \(k^2-144=0\), इसलिए \(k=\pm12\) और (k>0) से (k=12) है। परीक्षा में दी गई शर्त जरूर लगाएं।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2-16x+k=0\) के मूल समान हों, तो (k) का मान क्या होगा?
If \(x^2-16x+k=0\) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A (64)
B (16)
C (32)
D (256)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (256-4k=0) and (k=64). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (64). For equal roots, (D=0), so (256-4k=0) and (k=64). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (256-4k=0) और (k=64) है। परीक्षा में समान मूल का संकेत (D=0) है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि (D=0) और (a=3,b=-12), तो समान मूल क्या होगा?
If (D=0) and (a=3,b=-12), what will be the equal root?
#quadratic
#equal-roots
#formula
A (x=2)
B (x=-2)
C (x=4)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{12}{6}=2\). In exams, this short formula is useful when (D=0).
Step 2
Why this answer is correct
The correct answer is A. (x=2). The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{12}{6}=2\). In exams, this short formula is useful when (D=0).
Step 3
Exam Tip
समान मूल \(x=\frac{-b}{2a}\) होता है, इसलिए \(x=\frac{12}{6}=2\) है। परीक्षा में (D=0) पर यह छोटा सूत्र उपयोगी है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2+kx+25=0\) के समान मूल हैं और (k<0), तो (k) क्या होगा?
If \(x^2+kx+25=0\) has equal roots and (k<0), what is (k)?
#quadratic
#discriminant
#parameter
A ( -10)
B (10)
C (5)
D ( -5)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(k^2-100=0\), so \(k=\pm10\), and (k<0) gives (k=-10). In exams, apply the given condition.
Step 2
Why this answer is correct
The correct answer is A. ( -10). For equal roots, \(k^2-100=0\), so \(k=\pm10\), and (k<0) gives (k=-10). In exams, apply the given condition.
Step 3
Exam Tip
समान मूलों के लिए \(k^2-100=0\), इसलिए \(k=\pm10\) और (k<0) से (k=-10) है। परीक्षा में दी गई शर्त जरूर लगाएं।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2-12x+k=0\) के मूल समान हों, तो (k) का मान क्या होगा?
If \(x^2-12x+k=0\) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A (36)
B (12)
C (24)
D (144)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (144-4k=0) and (k=36). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (36). For equal roots, (D=0), so (144-4k=0) and (k=36). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (144-4k=0) और (k=36) है। परीक्षा में समान मूल का संकेत (D=0) है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि (D=0) और (a=2,b=-8), तो समान मूल क्या होगा?
If (D=0) and (a=2,b=-8), what will be the equal root?
#quadratic
#equal-roots
#formula
A (x=2)
B (x=-2)
C (x=4)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{8}{4}=2\). In exams, this short formula is useful when (D=0).
Step 2
Why this answer is correct
The correct answer is A. (x=2). The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{8}{4}=2\). In exams, this short formula is useful when (D=0).
Step 3
Exam Tip
समान मूल \(x=\frac{-b}{2a}\) होता है, इसलिए \(x=\frac{8}{4}=2\) है। परीक्षा में (D=0) पर यह छोटा सूत्र उपयोगी है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2+kx+16=0\) के समान मूल हैं और (k>0), तो (k) क्या होगा?
If \(x^2+kx+16=0\) has equal roots and (k>0), what is (k)?
#quadratic
#discriminant
#parameter
A (8)
B (4)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(k^2-64=0\), so \(k=\pm8\), and (k>0) gives (k=8). In exams, apply the given condition.
Step 2
Why this answer is correct
The correct answer is A. (8). For equal roots, \(k^2-64=0\), so \(k=\pm8\), and (k>0) gives (k=8). In exams, apply the given condition.
Step 3
Exam Tip
समान मूलों के लिए \(k^2-64=0\), इसलिए \(k=\pm8\) और (k>0) से (k=8) है। परीक्षा में दी गई शर्त जरूर लगाएं।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2-10x+k=0\) के मूल समान हों, तो (k) का मान क्या होगा?
If \(x^2-10x+k=0\) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
A (25)
B (10)
C (20)
D (100)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (100-4k=0) and (k=25). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (25). For equal roots, (D=0), so (100-4k=0) and (k=25). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (100-4k=0) और (k=25) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
Login to save your score, XP, coins and progress.
Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि (D=0), तो द्विघात समीकरण के मूल कैसे होते हैं?
If (D=0), what type of roots does a quadratic equation have?
#quadratic
#discriminant
#equal-roots
A समान वास्तविक मूल / Equal real roots
B दो अलग वास्तविक मूल / Two distinct real roots
C कोई वास्तविक मूल नहीं / No real roots
D अनंत मूल / Infinitely many roots
Explanation opens after your attempt
Correct Answer
A. समान वास्तविक मूल / Equal real roots
Step 1
Concept
When (D=0), both roots are equal. In exams, (D) quickly tells the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. समान वास्तविक मूल / Equal real roots. When (D=0), both roots are equal. In exams, (D) quickly tells the nature of roots.
Step 3
Exam Tip
(D=0) होने पर दोनों मूल समान होते हैं। परीक्षा में (D) से मूलों की प्रकृति तुरंत पता चलती है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x-2 +(m-2 )x+25=0) की जड़ें समान हैं, तो (m) के मान क्या हैं?
If (x-2 +(m-2 )x+25=0) has equal roots, what are the values of (m)?
#quadratic-roots
#equal-roots
#parameter-values
A (12) और (-8) / (12) and (-8)
B (10) और (-10) / (10) and (-10)
C (7) और (-3) / (7) and (-3)
D (5) और (-5) / (5) and (-5)
Explanation opens after your attempt
Correct Answer
A. (12) और (-8) / (12) and (-8)
Step 1
Concept
For equal roots, ((m-2 )2 -100=0). Thus \(m-2=\pm10\), so (m=12) or (m=-8).
Step 2
Why this answer is correct
The correct answer is A. (12) और (-8) / (12) and (-8). For equal roots, ((m-2 )2 -100=0). Thus \(m-2=\pm10\), so (m=12) or (m=-8).
Step 3
Exam Tip
समान जड़ों के लिए ((m-2 )2 -100=0) होगा। इसलिए \(m-2=\pm10\), अतः (m=12) या (m=-8)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x-2 -2(a+5)x+a-2 +18=0) की जड़ें समान हैं, तो (a) का मान क्या होगा?
If (x-2 -2(a+5)x+a-2 +18=0) has equal roots, what is the value of (a)?
#quadratic-roots
#equal-roots
#discriminant
A \(-\frac{7}{10}\)
B \(\frac{7}{10}\)
C \(-\frac{10}{7}\)
D \(\frac{10}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{7}{10}\)
Step 1
Concept
For equal roots, put (D=0). From (4(a+5)2 -4\(a^2+18\)=0), we get (10a+7=0), so \(a=-\frac{7}{10}\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{7}{10}\). For equal roots, put (D=0). From (4(a+5)2 -4\(a^2+18\)=0), we get (10a+7=0), so \(a=-\frac{7}{10}\).
Step 3
Exam Tip
समान जड़ों के लिए (D=0) रखते हैं। (4(a+5)2 -4\(a^2+18\)=0) से (10a+7=0), इसलिए \(a=-\frac{7}{10}\)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि (x-2 -(u+v+2)x+(u+1)(v+1)=0) की जड़ें समान हैं, तो सही कथन क्या है?
If (x-2 -(u+v+2)x+(u+1)(v+1)=0) has equal roots, which statement is correct?
#quadratic-roots
#equal-roots
#general-form
A (u+v=0)
B (uv=1)
C (u=v)
D (u=-v)
Explanation opens after your attempt
Step 1
Concept
The roots of this equation are (u+1) and (v+1). For equal roots, (u+1=v+1), so (u=v).
Step 2
Why this answer is correct
The correct answer is C. (u=v). The roots of this equation are (u+1) and (v+1). For equal roots, (u+1=v+1), so (u=v).
Step 3
Exam Tip
इस समीकरण की जड़ें (u+1) और (v+1) हैं। समान जड़ों के लिए (u+1=v+1), इसलिए (u=v)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि (x-2 +(m+1)x+16=0) की जड़ें समान हैं, तो (m) के मान क्या हैं?
If (x-2 +(m+1)x+16=0) has equal roots, what are the values of (m)?
#quadratic-roots
#equal-roots
#parameter-values
A (7) और (-9) / (7) and (-9)
B (8) और (-8) / (8) and (-8)
C (9) और (-7) / (9) and (-7)
D (15) और (-17) / (15) and (-17)
Explanation opens after your attempt
Correct Answer
A. (7) और (-9) / (7) and (-9)
Step 1
Concept
For equal roots, ((m+1)2 -64=0). Thus \(m+1=\pm8\), so (m=7) or (m=-9).
Step 2
Why this answer is correct
The correct answer is A. (7) और (-9) / (7) and (-9). For equal roots, ((m+1)2 -64=0). Thus \(m+1=\pm8\), so (m=7) or (m=-9).
Step 3
Exam Tip
समान जड़ों के लिए ((m+1)2 -64=0) होगा। इसलिए \(m+1=\pm8\), अतः (m=7) या (m=-9)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि (x-2 -2(a-4)x+a-2 -20=0) की जड़ें समान हैं, तो (a) का मान क्या होगा?
If (x-2 -2(a-4)x+a-2 -20=0) has equal roots, what is the value of (a)?
#quadratic-roots
#equal-roots
#discriminant
A \(\frac{7}{2}\)
B \(\frac{9}{2}\)
C \(\frac{11}{2}\)
D (5)
Explanation opens after your attempt
Correct Answer
B. \(\frac{9}{2}\)
Step 1
Concept
For equal roots, (D=0). From (4(a-4)2 -4\(a^2-20\)=0), we get \(a=\frac{9}{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{9}{2}\). For equal roots, (D=0). From (4(a-4)2 -4\(a^2-20\)=0), we get \(a=\frac{9}{2}\).
Step 3
Exam Tip
समान जड़ों के लिए (D=0) होता है। (4(a-4)2 -4\(a^2-20\)=0) से \(a=\frac{9}{2}\) मिलता है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि (x-2 -(u+v)x+uv=0) की जड़ें बराबर हैं, तो (u) और (v) के बारे में सही कथन क्या है?
If the roots of (x-2 -(u+v)x+uv=0) are equal, what is the correct statement about (u) and (v)?
#quadratic-roots
#equal-roots
#general-form
A (u=v)
B (u=-v)
C (uv=0)
D (u+v=0)
Explanation opens after your attempt
Step 1
Concept
The roots of this equation are (u) and (v). For equal roots, it is necessary that (u=v).
Step 2
Why this answer is correct
The correct answer is A. (u=v). The roots of this equation are (u) and (v). For equal roots, it is necessary that (u=v).
Step 3
Exam Tip
इस समीकरण की जड़ें (u) और (v) हैं। जड़ें बराबर होने के लिए (u=v) होना जरूरी है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि (x-2 +(m-5 )x+9=0) की जड़ें बराबर पर विपरीत चिह्न वाली नहीं हैं और समान हैं, तो (m) के मान क्या हैं?
If (x-2 +(m-5 )x+9=0) has equal roots that are not of opposite signs, what are the values of (m)?
#quadratic-roots
#equal-roots
#parameter-values
A (11) और (-1) / (11) and (-1)
B (5) और (-5) / (5) and (-5)
C (8) और (2) / (8) and (2)
D (14) और (-4) / (14) and (-4)
Explanation opens after your attempt
Correct Answer
A. (11) और (-1) / (11) and (-1)
Step 1
Concept
For equal roots, ((m-5 )2 -36=0). Thus \(m-5=\pm6\), so (m=11) or (m=-1).
Step 2
Why this answer is correct
The correct answer is A. (11) और (-1) / (11) and (-1). For equal roots, ((m-5 )2 -36=0). Thus \(m-5=\pm6\), so (m=11) or (m=-1).
Step 3
Exam Tip
समान जड़ों के लिए ((m-5 )2 -36=0) होगा। इसलिए \(m-5=\pm6\), अतः (m=11) या (m=-1)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि (x-2 -2(k+2)x+k-2 +5=0) की जड़ें समान हैं, तो (k) का मान क्या होगा?
If (x-2 -2(k+2)x+k-2 +5=0) has equal roots, what is the value of (k)?
#quadratic-roots
#equal-roots
#discriminant
A \(\frac{1}{4}\)
B (4)
C -\(\frac{1}{4}\)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{4}\)
Step 1
Concept
For equal roots, put (D=0). Simplifying (4(k+2)2 -4\(k^2+5\)=0) gives (4k-1=0), so \(k=\frac{1}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{4}\). For equal roots, put (D=0). Simplifying (4(k+2)2 -4\(k^2+5\)=0) gives (4k-1=0), so \(k=\frac{1}{4}\).
Step 3
Exam Tip
समान जड़ों के लिए (D=0) रखें। (4(k+2)2 -4\(k^2+5\)=0) से (4k+3=0) नहीं, बल्कि (4k-1=0) नहीं; सही सरलीकरण (4k-1=0) देता है, इसलिए \(k=\frac{1}{4}\)।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
((k-2)x-2 +4x+1=0) की जड़ें समान हों, तो (k) का मान क्या है?
If ((k-2)x-2 +4x+1=0) has equal roots, what is (k)?
#quadratic-roots
#equal-roots
#parameter
A (6)
B (4)
C (2)
D (-6)
Explanation opens after your attempt
Step 1
Concept
For equal roots, put (D=0). From (16-4(k-2)=0), we get (k=6).
Step 2
Why this answer is correct
The correct answer is A. (6). For equal roots, put (D=0). From (16-4(k-2)=0), we get (k=6).
Step 3
Exam Tip
समान जड़ों के लिए (D=0) रखें। (16-4(k-2)=0) से (k=6) मिलता है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
\(4x^2-4x+1=0\) की दोनों जड़ों का मान क्या है?
What is the value of both roots of \(4x^2-4x+1=0\)?
#quadratic-roots
#equal-roots
#perfect-square
A \(\frac{1}{2}\)
B \(-\frac{1}{2}\)
C (1)
D (-1)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
(4x-2 -4x+1=(2x-1)2 ). Therefore the equal root is \(x=\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). (4x-2 -4x+1=(2x-1)2 ). Therefore the equal root is \(x=\frac{1}{2}\).
Step 3
Exam Tip
(4x-2 -4x+1=(2x-1)2 ) है। इसलिए समान जड़ \(x=\frac{1}{2}\) है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
\(x^2+kx+16=0\) की जड़ें समान हों, तो (k) के संभव मान क्या हैं?
If \(x^2+kx+16=0\) has equal roots, what are the possible values of (k)?
#quadratic-roots
#equal-roots
#parameter
A (8) और (-8) / (8) and (-8)
B (4) और (-4) / (4) and (-4)
C (16) और (-16) / (16) and (-16)
D (2) और (-2) / (2) and (-2)
Explanation opens after your attempt
Correct Answer
A. (8) और (-8) / (8) and (-8)
Step 1
Concept
For equal roots, \(k^2-64=0\) must hold. Hence \(k=\pm8\).
Step 2
Why this answer is correct
The correct answer is A. (8) और (-8) / (8) and (-8). For equal roots, \(k^2-64=0\) must hold. Hence \(k=\pm8\).
Step 3
Exam Tip
समान जड़ों के लिए \(k^2-64=0\) होना चाहिए। अतः \(k=\pm8\) है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
सामान्य द्विघात समीकरण \(ax^2+bx+c=0\) में जड़ें समान हों, तो सही संबंध कौन-सा है?
For the general quadratic equation \(ax^2+bx+c=0\), which relation is correct when the roots are equal?
#quadratic-roots
#equal-roots
#standard-condition
A \(b^2=4ac\)
B \(b^2>4ac\)
C \(b^2<4ac\)
D (a+b+c=0)
Explanation opens after your attempt
Correct Answer
A. \(b^2=4ac\)
Step 1
Concept
For equal real roots, the discriminant \(D=b^2-4ac=0\). Therefore \(b^2=4ac\) is the correct relation.
Step 2
Why this answer is correct
The correct answer is A. \(b^2=4ac\). For equal real roots, the discriminant \(D=b^2-4ac=0\). Therefore \(b^2=4ac\) is the correct relation.
Step 3
Exam Tip
समान वास्तविक जड़ों के लिए विविक्तकर \(D=b^2-4ac=0\) होता है। इसलिए \(b^2=4ac\) सही संबंध है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
\(2x^2+\lambda x+8=0\) की जड़ें समान हों, तो \(\lambda\) के मान क्या होंगे?
If \(2x^2+\lambda x+8=0\) has equal roots, what are the values of \(\lambda\)?
#quadratic-roots
#equal-roots
#lambda
A (8) और (-8) / (8) and (-8)
B (4) और (-4) / (4) and (-4)
C (16) और (-16) / (16) and (-16)
D (2) और (-2) / (2) and (-2)
Explanation opens after your attempt
Correct Answer
A. (8) और (-8) / (8) and (-8)
Step 1
Concept
For equal roots, put (D=0). From \(\lambda^2-64=0\), we get \(\lambda=\pm8\).
Step 2
Why this answer is correct
The correct answer is A. (8) और (-8) / (8) and (-8). For equal roots, put (D=0). From \(\lambda^2-64=0\), we get \(\lambda=\pm8\).
Step 3
Exam Tip
समान जड़ों के लिए (D=0) रखें। \(\lambda^2-64=0\) से \(\lambda=\pm8\) मिलता है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(x-2 +2(k-1)x+k+5=0) की जड़ें समान हों, तो (k) के मान कौन-से हैं?
If (x-2 +2(k-1)x+k+5=0) has equal roots, what are the values of (k)?
#quadratic-roots
#equal-roots
#parameter-values
A (4) और (-1) / (4) and (-1)
B (4) और (1) / (4) and (1)
C (-4) और (1) / (-4) and (1)
D (-5) और (4) / (-5) and (4)
Explanation opens after your attempt
Correct Answer
A. (4) और (-1) / (4) and (-1)
Step 1
Concept
For equal roots, put (D=0). This gives \(k^2-3k-4=0\), so (k=4) or (k=-1).
Step 2
Why this answer is correct
The correct answer is A. (4) और (-1) / (4) and (-1). For equal roots, put (D=0). This gives \(k^2-3k-4=0\), so (k=4) or (k=-1).
Step 3
Exam Tip
समान जड़ों के लिए (D=0) रखें। इससे \(k^2-3k-4=0\) मिलता है, इसलिए (k=4) या (k=-1)।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(kx-2 -2(k+1)x+(k+4)=0) की जड़ें समान हों, तो (k) का मान क्या है?
For (kx-2 -2(k+1)x+(k+4)=0) to have equal roots, what is the value of (k)?
#quadratic-roots
#equal-roots
#discriminant
A \(\frac{1}{2}\)
B \(-\frac{1}{2}\)
C (1)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
For equal roots, the discriminant (D=0). Since (D=4(1-2k)), we get \(k=\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). For equal roots, the discriminant (D=0). Since (D=4(1-2k)), we get \(k=\frac{1}{2}\).
Step 3
Exam Tip
समान जड़ों के लिए विविक्तकर (D=0) होता है। (D=4(1-2k)) रखने पर \(k=\frac{1}{2}\) आता है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि \(kx^2-8x+16=0\) के बराबर मूल हैं और \(k\ne0\) है तो (k) का मान क्या है?
If \(kx^2-8x+16=0\) has equal roots and \(k\ne0\), what is the value of (k)?
#roots
#parameter
#discriminant
A (1)
B (2)
C (4)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
For equal roots (D=0). From (64-64k=0), (k=1).
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots (D=0). From (64-64k=0), (k=1).
Step 3
Exam Tip
बराबर मूलों के लिए (D=0) होता है। (64-64k=0) से (k=1) है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि \(kx^2-6x+9=0\) के बराबर मूल हैं और \(k\ne0\) है तो (k) का मान क्या है?
If \(kx^2-6x+9=0\) has equal roots and \(k\ne0\), what is the value of (k)?
#roots
#parameter
#discriminant
A (1)
B (2)
C (3)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
For equal roots (D=0). From (36-36k=0), (k=1).
Step 2
Why this answer is correct
The correct answer is A. (1). For equal roots (D=0). From (36-36k=0), (k=1).
Step 3
Exam Tip
बराबर मूलों के लिए (D=0) होता है। (36-36k=0) से (k=1) है।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि समीकरण \(x^2+bx+144=0\) के दोनों मूल समान हैं और उनका मान (-12) है, तो (b) क्या है?
If both roots of \(x^2+bx+144=0\) are equal and their value is (-12), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#expert
A (24)
B (-24)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-12), so the sum is (-24). Here the sum of roots is (-b), so (b=24).
Step 2
Why this answer is correct
The correct answer is A. (24). Both roots are (-12), so the sum is (-24). Here the sum of roots is (-b), so (b=24).
Step 3
Exam Tip
दोनों मूल (-12) हैं, इसलिए योग (-24) है। यहाँ मूलों का योग (-b) है, अतः (b=24)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-2mx+64=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?
If the roots of \(x^2-2mx+64=0\) are equal, what are the possible values of (m)?
#quadratic-equations
#equal-roots
#discriminant
#expert
A \(m=\pm8\)
B \(m=\pm16\)
C (m=8)
D (m=-8)
Explanation opens after your attempt
Correct Answer
A. \(m=\pm8\)
Step 1
Concept
For equal roots, (D=0) is needed. Here ((-2m)2 -256=0), so \(m=\pm8\).
Step 2
Why this answer is correct
The correct answer is A. \(m=\pm8\). For equal roots, (D=0) is needed. Here ((-2m)2 -256=0), so \(m=\pm8\).
Step 3
Exam Tip
समान मूलों के लिए (D=0) चाहिए। यहाँ ((-2m)2 -256=0), इसलिए \(m=\pm8\)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि समीकरण \(x^2+bx+100=0\) के दोनों मूल समान हैं और उनका मान (-10) है, तो (b) क्या है?
If both roots of \(x^2+bx+100=0\) are equal and their value is (-10), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#expert
A (20)
B (-20)
C (10)
D (-10)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-10), so the sum is (-20). Here the sum of roots is (-b), so (b=20).
Step 2
Why this answer is correct
The correct answer is A. (20). Both roots are (-10), so the sum is (-20). Here the sum of roots is (-b), so (b=20).
Step 3
Exam Tip
दोनों मूल (-10) हैं, इसलिए योग (-20) है। यहाँ मूलों का योग (-b) है, अतः (b=20)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-2mx+49=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?
If the roots of \(x^2-2mx+49=0\) are equal, what are the possible values of (m)?
#quadratic-equations
#equal-roots
#discriminant
#expert
A \(m=\pm7\)
B \(m=\pm14\)
C (m=7)
D (m=-7)
Explanation opens after your attempt
Correct Answer
A. \(m=\pm7\)
Step 1
Concept
For equal roots, (D=0) is needed. Here ((-2m)2 -196=0), so \(m=\pm7\).
Step 2
Why this answer is correct
The correct answer is A. \(m=\pm7\). For equal roots, (D=0) is needed. Here ((-2m)2 -196=0), so \(m=\pm7\).
Step 3
Exam Tip
समान मूलों के लिए (D=0) चाहिए। यहाँ ((-2m)2 -196=0), इसलिए \(m=\pm7\)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि समीकरण \(x^2+bx+64=0\) के दोनों मूल समान हैं और उनका मान (-8) है, तो (b) क्या है?
If both roots of \(x^2+bx+64=0\) are equal and their value is (-8), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#expert
A (16)
B (-16)
C (8)
D (-8)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-8), so the sum is (-16). Here the sum of roots is (-b), so (b=16).
Step 2
Why this answer is correct
The correct answer is A. (16). Both roots are (-8), so the sum is (-16). Here the sum of roots is (-b), so (b=16).
Step 3
Exam Tip
दोनों मूल (-8) हैं, इसलिए योग (-16) है। यहाँ मूलों का योग (-b) है, अतः (b=16)।
Login to save your score, XP, coins and progress.
Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2-2mx+36=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?
If the roots of \(x^2-2mx+36=0\) are equal, what are the possible values of (m)?
#quadratic-equations
#equal-roots
#discriminant
#expert
A \(m=\pm6\)
B \(m=\pm12\)
C (m=6)
D (m=-6)
Explanation opens after your attempt
Correct Answer
A. \(m=\pm6\)
Step 1
Concept
For equal roots, (D=0), so ((-2m)2 -144=0). This gives \(m^2=36\) and \(m=\pm6\).
Step 2
Why this answer is correct
The correct answer is A. \(m=\pm6\). For equal roots, (D=0), so ((-2m)2 -144=0). This gives \(m^2=36\) and \(m=\pm6\).
Step 3
Exam Tip
समान मूलों के लिए (D=0), अतः ((-2m)2 -144=0) होगा। इससे \(m^2=36\) और \(m=\pm6\) है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि समीकरण \(x^2+bx+49=0\) के दोनों मूल समान हैं और उनका मान (-7) है, तो (b) क्या है?
If both roots of \(x^2+bx+49=0\) are equal and their value is (-7), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#hard
A (14)
B (-14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-7), so their sum is (-14). Here the sum of roots is (-b), so (b=14).
Step 2
Why this answer is correct
The correct answer is A. (14). Both roots are (-7), so their sum is (-14). Here the sum of roots is (-b), so (b=14).
Step 3
Exam Tip
दोनों मूल (-7) हैं, इसलिए योग (-14) है। यहाँ मूलों का योग (-b) है, अतः (b=14)।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-2kx+25=0\) के मूल समान हैं, तो (k) के संभावित मान क्या हैं?
If the roots of \(x^2-2kx+25=0\) are equal, what are the possible values of (k)?
#quadratic-equations
#equal-roots
#discriminant
#hard
A \(k=\pm5\)
B \(k=\pm10\)
C (k=5)
D (k=-5)
Explanation opens after your attempt
Correct Answer
A. \(k=\pm5\)
Step 1
Concept
For equal roots, (D=0), so ((-2k)2 -100=0). This gives \(k^2=25\) and \(k=\pm5\).
Step 2
Why this answer is correct
The correct answer is A. \(k=\pm5\). For equal roots, (D=0), so ((-2k)2 -100=0). This gives \(k^2=25\) and \(k=\pm5\).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((-2k)2 -100=0) मिलता है। इससे \(k^2=25\) और \(k=\pm5\) है।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि समीकरण \(x^2+bx+25=0\) के दोनों मूल समान हैं और उनका मान (-5) है, तो (b) क्या है?
If both roots of \(x^2+bx+25=0\) are equal and their value is (-5), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#hard
A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-5), so their sum is (-10). Here the sum of roots is (-b), so (b=10).
Step 2
Why this answer is correct
The correct answer is A. (10). Both roots are (-5), so their sum is (-10). Here the sum of roots is (-b), so (b=10).
Step 3
Exam Tip
दोनों मूल (-5) हैं, इसलिए योग (-10) है। यहाँ मूलों का योग (-b) है, अतः (b=10)।
Login to save your score, XP, coins and progress.
Question
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-2kx+16=0\) के मूल समान हैं, तो (k) के संभावित मान क्या हैं?
If the roots of \(x^2-2kx+16=0\) are equal, what are the possible values of (k)?
#quadratic-equations
#equal-roots
#discriminant
#hard
A \(k=\pm4\)
B \(k=\pm8\)
C (k=4)
D (k=-4)
Explanation opens after your attempt
Correct Answer
A. \(k=\pm4\)
Step 1
Concept
For equal roots, (D=0), so ((-2k)2 -64=0). This gives \(k^2=16\) and \(k=\pm4\).
Step 2
Why this answer is correct
The correct answer is A. \(k=\pm4\). For equal roots, (D=0), so ((-2k)2 -64=0). This gives \(k^2=16\) and \(k=\pm4\).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((-2k)2 -64=0) मिलता है। इससे \(k^2=16\) और \(k=\pm4\) है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि द्विघात समीकरण \(x^2-18x+k=0\) के मूल समान हैं, तो (k) क्या होगा?
If the roots of \(x^2-18x+k=0\) are equal, what is (k)?
#quadratic-equations
#equal-roots
#discriminant
#medium
A (18)
B (81)
C (162)
D (324)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (324-4k=0) and (k=81). For equal roots, set the discriminant to zero.
Step 2
Why this answer is correct
The correct answer is B. (81). For equal roots, (D=0), so (324-4k=0) and (k=81). For equal roots, set the discriminant to zero.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (324-4k=0) और (k=81)। समान मूल की शर्त में विवेचक शून्य रखें।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+ux+64=0\) के मूल (8) और (8) हैं, तो (u) का मान क्या होगा?
If the roots of \(x^2+ux+64=0\) are (8) and (8), what is the value of (u)?
#quadratic-equations
#equal-roots
#parameter
#medium
A (16)
B (-16)
C (8)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (16), and in \(x^2+ux+64=0\), the sum is (-u). Therefore (u=-16).
Step 2
Why this answer is correct
The correct answer is B. (-16). The sum of roots is (16), and in \(x^2+ux+64=0\), the sum is (-u). Therefore (u=-16).
Step 3
Exam Tip
मूलों का योग (16) है और \(x^2+ux+64=0\) में योग (-u) होता है। इसलिए (u=-16) है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(25x^2-20x+4=0\) का विवेचक (D) क्या है?
What is the discriminant (D) of \(25x^2-20x+4=0\)?
#quadratic-equations
#discriminant
#equal-roots
#medium
A (0)
B (20)
C (100)
D (-20)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-20)2 -4\cdot25\cdot4=400-400=0). (D=0) indicates equal roots.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=(-20)2 -4\cdot25\cdot4=400-400=0). (D=0) indicates equal roots.
Step 3
Exam Tip
यहाँ (D=(-20)2 -4\cdot25\cdot4=400-400=0) है। (D=0) समान मूलों का संकेत देता है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि द्विघात समीकरण \(x^2-14x+k=0\) के मूल समान हैं, तो (k) क्या होगा?
If the roots of \(x^2-14x+k=0\) are equal, what is (k)?
#quadratic-equations
#equal-roots
#discriminant
#medium
A (14)
B (49)
C (98)
D (196)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (196-4k=0) and (k=49). For equal roots, set the discriminant to zero.
Step 2
Why this answer is correct
The correct answer is B. (49). For equal roots, (D=0), so (196-4k=0) and (k=49). For equal roots, set the discriminant to zero.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (196-4k=0) और (k=49)। समान मूल की शर्त में विवेचक शून्य रखें।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+rx+36=0\) के मूल (6) और (6) हैं, तो (r) का मान क्या होगा?
If the roots of \(x^2+rx+36=0\) are (6) and (6), what is the value of (r)?
#quadratic-equations
#equal-roots
#parameter
#medium
A (12)
B (-12)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (12), and in \(x^2+rx+36=0\) the sum is (-r). Therefore (r=-12).
Step 2
Why this answer is correct
The correct answer is B. (-12). The sum of roots is (12), and in \(x^2+rx+36=0\) the sum is (-r). Therefore (r=-12).
Step 3
Exam Tip
मूलों का योग (12) है और \(x^2+rx+36=0\) में योग (-r) होता है। इसलिए (r=-12) है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(9x^2-12x+4=0\) का विवेचक (D) क्या है?
What is the discriminant (D) of \(9x^2-12x+4=0\)?
#quadratic-equations
#discriminant
#equal-roots
#medium
A (0)
B (12)
C (24)
D (-12)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-12)2 -4\cdot9\cdot4=144-144=0). Even if (b) is negative, \(b^2\) is positive.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=(-12)2 -4\cdot9\cdot4=144-144=0). Even if (b) is negative, \(b^2\) is positive.
Step 3
Exam Tip
यहाँ (D=(-12)2 -4\cdot9\cdot4=144-144=0) है। (b) ऋणात्मक हो तो भी \(b^2\) धनात्मक होता है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि द्विघात समीकरण \(x^2-6x+k=0\) के मूल समान हैं, तो (k) क्या होगा?
If the roots of \(x^2-6x+k=0\) are equal, what is (k)?
#quadratic-equations
#equal-roots
#discriminant
#medium
A (6)
B (9)
C (12)
D (36)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (36-4k=0) and (k=9). Set the discriminant to zero for equal roots.
Step 2
Why this answer is correct
The correct answer is B. (9). For equal roots, (D=0), so (36-4k=0) and (k=9). Set the discriminant to zero for equal roots.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (36-4k=0) और (k=9)। समान मूल की शर्त में विवेचक शून्य रखें।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2+px+16=0\) के मूल (4) और (4) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+16=0\) are (4) and (4), what is the value of (p)?
#quadratic-equations
#equal-roots
#parameter
#medium
A (8)
B (-8)
C (16)
D (-16)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (8), and in \(x^2+px+16=0\) the sum is (-p). Therefore (p=-8).
Step 2
Why this answer is correct
The correct answer is B. (-8). The sum of roots is (8), and in \(x^2+px+16=0\) the sum is (-p). Therefore (p=-8).
Step 3
Exam Tip
मूलों का योग (8) है और \(x^2+px+16=0\) में योग (-p) होता है। इसलिए (p=-8) है।
Login to save your score, XP, coins and progress.
Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(4x^2+4x+1=0\) का विवेचक (D) क्या है?
What is the discriminant (D) of \(4x^2+4x+1=0\)?
#quadratic-equations
#discriminant
#equal-roots
#medium
A (0)
B (8)
C (16)
D (-16)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=4^2-4\cdot4\cdot1=0\). Correctly identifying (a,b,c) is necessary for the discriminant.
Step 2
Why this answer is correct
The correct answer is A. (0). Here \(D=b^2-4ac=4^2-4\cdot4\cdot1=0\). Correctly identifying (a,b,c) is necessary for the discriminant.
Step 3
Exam Tip
यहाँ \(D=b^2-4ac=4^2-4\cdot4\cdot1=0\) है। विवेचक में (a,b,c) सही पहचानना जरूरी है।
Login to save your score, XP, coins and progress.
Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी द्विघात समीकरण का विवेचक (D=0) है तो मूल कैसे होंगे?
If the discriminant (D=0) for a quadratic equation, how will the roots be?
#quadratic-equations
#discriminant
#equal-roots
A दो भिन्न वास्तविक मूल / Two distinct real roots
B दो समान वास्तविक मूल / Two equal real roots
C कोई वास्तविक मूल नहीं / No real roots
D तीन वास्तविक मूल / Three real roots
Explanation opens after your attempt
Correct Answer
B. दो समान वास्तविक मूल / Two equal real roots
Step 1
Concept
When (D=0), both real roots are equal. In such questions, compare (D) with (0).
Step 2
Why this answer is correct
The correct answer is B. दो समान वास्तविक मूल / Two equal real roots. When (D=0), both real roots are equal. In such questions, compare (D) with (0).
Step 3
Exam Tip
(D=0) होने पर दोनों वास्तविक मूल समान होते हैं। ऐसे प्रश्नों में (D) की तुलना (0) से करें।
Login to save your score, XP, coins and progress.
