Question 31/60
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2-2x+5=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?
What form is obtained by completing the square in \(x^2-2x+5=0\)?
#quadratic
#completing-square
#no-real-roots
A ((x-1)2 +4=0)
B ((x+1)2 +4=0)
C ((x-1)2 -4=0)
D ((x+2)2 +1=0)
Explanation opens after your attempt
Correct Answer
A. ((x-1)2 +4=0)
Step 1
Concept
(x-2 -2x+5=(x-1)2 +4), so no real roots are obtained. In exams, the completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. ((x-1)2 +4=0). (x-2 -2x+5=(x-1)2 +4), so no real roots are obtained. In exams, the completed square form also shows the nature of roots.
Step 3
Exam Tip
(x-2 -2x+5=(x-1)2 +4), इसलिए वास्तविक मूल नहीं मिलते। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति समझ सकते हैं।
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Question 32/60
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2-2x+5=0\) के वास्तविक मूलों के बारे में सही कथन क्या है?
What is the correct statement about real roots of \(x^2-2x+5=0\)?
#quadratic
#discriminant
#no-real-roots
A कोई वास्तविक मूल नहीं / No real roots
B दो समान वास्तविक मूल / Two equal real roots
C दो अलग वास्तविक मूल / Two distinct real roots
D एक मूल (0) / One root (0)
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक मूल नहीं / No real roots
Step 1
Concept
Here (D=(-2)2 -4(1)(5)=-16<0), so there are no real roots. In exams, (D<0) means no real solution.
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक मूल नहीं / No real roots. Here (D=(-2)2 -4(1)(5)=-16<0), so there are no real roots. In exams, (D<0) means no real solution.
Step 3
Exam Tip
यहां (D=(-2)2 -4(1)(5)=-16<0), इसलिए वास्तविक मूल नहीं हैं। परीक्षा में (D<0) होने पर वास्तविक हल नहीं मिलता।
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Question 33/60
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2+36=0\) के वास्तविक मूलों के बारे में सही कथन क्या है?
What is the correct statement about the real roots of \(x^2+36=0\)?
#quadratic
#no-real-roots
#square-root-method
A कोई वास्तविक मूल नहीं / No real roots
B दो वास्तविक मूल (6) और (-6) / Two real roots (6) and (-6)
C एक वास्तविक मूल (36) / One real root (36)
D दो समान वास्तविक मूल (0) / Two equal real roots (0)
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक मूल नहीं / No real roots
Step 1
Concept
\(x^2=-36\) is not possible in real numbers. In exams, \(x^2\) is not negative for real (x).
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक मूल नहीं / No real roots. \(x^2=-36\) is not possible in real numbers. In exams, \(x^2\) is not negative for real (x).
Step 3
Exam Tip
\(x^2=-36\) वास्तविक संख्याओं में संभव नहीं है। परीक्षा में \(x^2\) का मान वास्तविक (x) के लिए ऋणात्मक नहीं होता।
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Question 34/60
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि किसी द्विघात समीकरण में (D=-9) हो, तो कौनसा निष्कर्ष सही है?
If a quadratic equation has (D=-9), which conclusion is correct?
#quadratic
#discriminant
#no-real-roots
A वास्तविक मूल नहीं होंगे / There will be no real roots
B दो समान वास्तविक मूल होंगे / There will be two equal real roots
C दो अलग वास्तविक मूल होंगे / There will be two distinct real roots
D एक मूल (0) होगा / One root will be (0)
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं होंगे / There will be no real roots
Step 1
Concept
When (D<0), no real square root is obtained. In exams, remember the meaning of a negative discriminant.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं होंगे / There will be no real roots. When (D<0), no real square root is obtained. In exams, remember the meaning of a negative discriminant.
Step 3
Exam Tip
(D<0) होने पर वास्तविक वर्गमूल नहीं मिलता। परीक्षा में ऋणात्मक विविक्तकर का अर्थ याद रखें।
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Question 35/60
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2+25=0\) के वास्तविक मूलों के बारे में सही कथन क्या है?
What is the correct statement about the real roots of \(x^2+25=0\)?
#quadratic
#no-real-roots
#square-root-method
A कोई वास्तविक मूल नहीं / No real roots
B दो वास्तविक मूल (5) और (-5) / Two real roots (5) and (-5)
C एक वास्तविक मूल (25) / One real root (25)
D दो समान वास्तविक मूल (0) / Two equal real roots (0)
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक मूल नहीं / No real roots
Step 1
Concept
\(x^2=-25\) is not possible in real numbers. In exams, \(x^2\) is not negative for real (x).
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक मूल नहीं / No real roots. \(x^2=-25\) is not possible in real numbers. In exams, \(x^2\) is not negative for real (x).
Step 3
Exam Tip
\(x^2=-25\) वास्तविक संख्याओं में संभव नहीं है। परीक्षा में \(x^2\) का मान वास्तविक (x) के लिए ऋणात्मक नहीं होता।
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Question 36/60
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि किसी द्विघात समीकरण में (D=-4) हो, तो कौनसा निष्कर्ष सही है?
If a quadratic equation has (D=-4), which conclusion is correct?
#quadratic
#discriminant
#no-real-roots
A वास्तविक मूल नहीं होंगे / There will be no real roots
B दो समान वास्तविक मूल होंगे / There will be two equal real roots
C दो अलग वास्तविक मूल होंगे / There will be two distinct real roots
D एक मूल (0) होगा / One root will be (0)
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं होंगे / There will be no real roots
Step 1
Concept
When (D<0), no real square root is obtained. In exams, remember the meaning of a negative discriminant.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं होंगे / There will be no real roots. When (D<0), no real square root is obtained. In exams, remember the meaning of a negative discriminant.
Step 3
Exam Tip
(D<0) होने पर वास्तविक वर्गमूल नहीं मिलता। परीक्षा में ऋणात्मक विविक्तकर का अर्थ याद रखें।
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Question 37/60
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2+9=0\) के वास्तविक मूलों के बारे में सही कथन क्या है?
What is the correct statement about the real roots of \(x^2+9=0\)?
#quadratic
#no-real-roots
#square-root-method
A कोई वास्तविक मूल नहीं / No real roots
B दो वास्तविक मूल (3) और (-3) / Two real roots (3) and (-3)
C एक वास्तविक मूल (9) / One real root (9)
D दो समान वास्तविक मूल (0) / Two equal real roots (0)
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक मूल नहीं / No real roots
Step 1
Concept
\(x^2=-9\) gives no solution in real numbers. In exams, remember that \(x^2\) cannot be negative for real (x).
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक मूल नहीं / No real roots. \(x^2=-9\) gives no solution in real numbers. In exams, remember that \(x^2\) cannot be negative for real (x).
Step 3
Exam Tip
\(x^2=-9\) से वास्तविक संख्या में हल नहीं मिलता। परीक्षा में \(x^2\) ऋणात्मक नहीं हो सकता यह याद रखें।
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Question 38/60
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(x-2 -2x+(p+3)=0) की वास्तविक जड़ें न हों, इसके लिए (p) पर सही शर्त क्या है?
For (x-2 -2x+(p+3)=0) to have no real roots, what is the correct condition on (p)?
#quadratic-roots
#no-real-roots
#inequality
A (p>-2)
B \(p\ge -2\)
C (p<-2)
D \(p\le -2\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is required. Here (D=-4(p+2)), so (p>-2).
Step 2
Why this answer is correct
The correct answer is A. (p>-2). For no real roots, (D<0) is required. Here (D=-4(p+2)), so (p>-2).
Step 3
Exam Tip
वास्तविक जड़ें न होने के लिए (D<0) चाहिए। यहाँ (D=-4(p+2)), इसलिए (p>-2) है।
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Question 39/60
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
\(5x^2-2x+1=0\) की जड़ों के बारे में सही कथन कौन-सा है?
Which statement is correct about the roots of \(5x^2-2x+1=0\)?
#quadratic-roots
#no-real-roots
#discriminant
A दो समान वास्तविक / Two equal real
B दो वास्तविक और भिन्न / Two real and distinct
C वास्तविक जड़ें नहीं / No real roots
D दोनों जड़ें (0) हैं / Both roots are (0)
Explanation opens after your attempt
Correct Answer
C. वास्तविक जड़ें नहीं / No real roots
Step 1
Concept
Here (D=(-2)2 -4(5)(1)=-16<0). Therefore the equation has no real roots.
Step 2
Why this answer is correct
The correct answer is C. वास्तविक जड़ें नहीं / No real roots. Here (D=(-2)2 -4(5)(1)=-16<0). Therefore the equation has no real roots.
Step 3
Exam Tip
यहाँ (D=(-2)2 -4(5)(1)=-16<0) है। इसलिए इस समीकरण की वास्तविक जड़ें नहीं हैं।
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Question 40/60
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि समीकरण (x-2 -4x+(m+4)=0) के वास्तविक मूल नहीं हैं तो (m) के लिए कौन सी शर्त सही है?
If (x-2 -4x+(m+4)=0) has no real roots, which condition on (m) is correct?
#roots
#no_real_roots
#parameter_condition
A (m>0)
B (m<0)
C (m=0)
D \(m\le0\)
Explanation opens after your attempt
Step 1
Concept
For no real roots (D<0) is required. From (16-4(m+4)<0), we get (m>0).
Step 2
Why this answer is correct
The correct answer is A. (m>0). For no real roots (D<0) is required. From (16-4(m+4)<0), we get (m>0).
Step 3
Exam Tip
वास्तविक मूल नहीं होने के लिए (D<0) चाहिए। (16-4(m+4)<0) से (m>0) मिलता है।
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Question 41/60
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
समीकरण \(x^2+4x+13=0\) के वास्तविक मूलों की संख्या कितनी है?
How many real roots does \(x^2+4x+13=0\) have?
#roots
#no_real_roots
#discriminant
A (0)
B (1)
C (2)
D अनंत / Infinitely many
Explanation opens after your attempt
Step 1
Concept
Here (D=16-52=-36<0). Therefore the number of real roots is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=16-52=-36<0). Therefore the number of real roots is (0).
Step 3
Exam Tip
यहां (D=16-52=-36<0) है। इसलिए वास्तविक मूलों की संख्या (0) है।
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Question 42/60
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि समीकरण (x-2 -2x+(m+1)=0) के वास्तविक मूल नहीं हैं तो (m) के लिए कौन सी शर्त सही है?
If (x-2 -2x+(m+1)=0) has no real roots, which condition on (m) is correct?
#roots
#no_real_roots
#parameter_condition
A (m>0)
B (m<0)
C (m=0)
D \(m\le0\)
Explanation opens after your attempt
Step 1
Concept
For no real roots (D<0) is required. From (4-4(m+1)<0), we get (m>0).
Step 2
Why this answer is correct
The correct answer is A. (m>0). For no real roots (D<0) is required. From (4-4(m+1)<0), we get (m>0).
Step 3
Exam Tip
वास्तविक मूल नहीं होने के लिए (D<0) चाहिए। (4-4(m+1)<0) से (m>0) मिलता है।
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Question 43/60
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
समीकरण \(x^2+2x+5=0\) के वास्तविक मूलों की संख्या कितनी है?
How many real roots does \(x^2+2x+5=0\) have?
#roots
#no_real_roots
#discriminant
A (0)
B (1)
C (2)
D अनंत / Infinitely many
Explanation opens after your attempt
Step 1
Concept
Here (D=4-20=-16<0). Therefore the number of real roots is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=4-20=-16<0). Therefore the number of real roots is (0).
Step 3
Exam Tip
यहां (D=4-20=-16<0) है। इसलिए वास्तविक मूलों की संख्या (0) है।
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Question 44/60
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
समीकरण \(x^2-6x+20=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?
Which statement is correct about the real roots of \(x^2-6x+20=0\)?
#roots
#no_real_roots
#discriminant
A दो भिन्न वास्तविक मूल हैं / It has two distinct real roots
B दो बराबर वास्तविक मूल हैं / It has two equal real roots
C कोई वास्तविक मूल नहीं है / It has no real roots
D मूल (6) और (20) हैं / The roots are (6) and (20)
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं है / It has no real roots
Step 1
Concept
Here (D=(-6)2 -4(1)(20)=-44<0). Therefore there are no real roots.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं है / It has no real roots. Here (D=(-6)2 -4(1)(20)=-44<0). Therefore there are no real roots.
Step 3
Exam Tip
यहां (D=(-6)2 -4(1)(20)=-44<0) है। इसलिए कोई वास्तविक मूल नहीं है।
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Question 45/60
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
समीकरण \(x^2-4x+13=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?
Which statement is correct about the real roots of \(x^2-4x+13=0\)?
#roots
#no_real_roots
#discriminant
A दो भिन्न वास्तविक मूल हैं / It has two distinct real roots
B दो बराबर वास्तविक मूल हैं / It has two equal real roots
C कोई वास्तविक मूल नहीं है / It has no real roots
D मूल (4) और (13) हैं / The roots are (4) and (13)
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं है / It has no real roots
Step 1
Concept
Here (D=(-4)2 -4(1)(13)=-36<0). Therefore there are no real roots.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं है / It has no real roots. Here (D=(-4)2 -4(1)(13)=-36<0). Therefore there are no real roots.
Step 3
Exam Tip
यहां (D=(-4)2 -4(1)(13)=-36<0) है। इसलिए कोई वास्तविक मूल नहीं है।
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Question 46/60
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि (D<0) है तो किसी द्विघात समीकरण के वास्तविक मूलों की संख्या कितनी होगी?
If (D<0), how many real roots will a quadratic equation have?
#roots
#discriminant
#no_real_roots
A (0)
B (1)
C (2)
D अनगिनत / Infinitely many
Explanation opens after your attempt
Step 1
Concept
When (D<0), there are no real roots. Therefore the number of real roots is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). When (D<0), there are no real roots. Therefore the number of real roots is (0).
Step 3
Exam Tip
(D<0) होने पर वास्तविक मूल नहीं होते। इसलिए वास्तविक मूलों की संख्या (0) होगी।
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Question 47/60
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
समीकरण \(x^2-2x+10=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?
Which statement is correct about the real roots of \(x^2-2x+10=0\)?
#roots
#no_real_roots
#discriminant
A दो भिन्न वास्तविक मूल हैं / It has two distinct real roots
B दो बराबर वास्तविक मूल हैं / It has two equal real roots
C कोई वास्तविक मूल नहीं है / It has no real roots
D मूल (2) और (10) हैं / The roots are (2) and (10)
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं है / It has no real roots
Step 1
Concept
Here (D=(-2)2 -4(1)(10)=-36<0). Therefore there are no real roots.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं है / It has no real roots. Here (D=(-2)2 -4(1)(10)=-36<0). Therefore there are no real roots.
Step 3
Exam Tip
यहां (D=(-2)2 -4(1)(10)=-36<0) है। इसलिए कोई वास्तविक मूल नहीं है।
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Question 48/60
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
समीकरण \(x^2+36=0\) के वास्तविक मूलों की संख्या कितनी है?
How many real roots does \(x^2+36=0\) have?
#roots
#no_real_roots
#number_of_roots
A (2)
B (1)
C (0)
D (36)
Explanation opens after your attempt
Step 1
Concept
For a real number, \(x^2\ge0\). Therefore \(x^2+36=0\) has no real root.
Step 2
Why this answer is correct
The correct answer is C. (0). For a real number, \(x^2\ge0\). Therefore \(x^2+36=0\) has no real root.
Step 3
Exam Tip
वास्तविक संख्या के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+36=0\) का कोई वास्तविक मूल नहीं है।
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Question 49/60
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
समीकरण \(x^2+25=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?
Which statement is correct about the real roots of \(x^2+25=0\)?
#roots
#no_real_roots
#concept
A दो वास्तविक मूल हैं / It has two real roots
B एक वास्तविक मूल है / It has one real root
C कोई वास्तविक मूल नहीं है / It has no real roots
D मूल (5) और (-5) हैं / The roots are (5) and (-5)
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं है / It has no real roots
Step 1
Concept
For real (x), \(x^2\ge0\). Therefore \(x^2+25=0\) has no real root.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं है / It has no real roots. For real (x), \(x^2\ge0\). Therefore \(x^2+25=0\) has no real root.
Step 3
Exam Tip
वास्तविक (x) के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+25=0\) का कोई वास्तविक मूल नहीं है।
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Question 50/60
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
समीकरण \(x^2+16=0\) के वास्तविक मूलों की संख्या कितनी है?
How many real roots does \(x^2+16=0\) have?
#roots
#no_real_roots
#number_of_roots
A (2)
B (1)
C (0)
D (16)
Explanation opens after your attempt
Step 1
Concept
For a real number, \(x^2\ge0\). Therefore \(x^2+16=0\) has no real root.
Step 2
Why this answer is correct
The correct answer is C. (0). For a real number, \(x^2\ge0\). Therefore \(x^2+16=0\) has no real root.
Step 3
Exam Tip
वास्तविक संख्या के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+16=0\) का कोई वास्तविक मूल नहीं है।
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Question 51/60
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
समीकरण \(x^2+9=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?
Which statement is correct about the real roots of \(x^2+9=0\)?
#roots
#no_real_roots
#concept
A दो वास्तविक मूल हैं / It has two real roots
B एक वास्तविक मूल है / It has one real root
C कोई वास्तविक मूल नहीं है / It has no real roots
D मूल (3) और (-3) हैं / The roots are (3) and (-3)
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं है / It has no real roots
Step 1
Concept
For any real (x), \(x^2\ge0\). So \(x^2+9=0\) is not satisfied by any real number.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं है / It has no real roots. For any real (x), \(x^2\ge0\). So \(x^2+9=0\) is not satisfied by any real number.
Step 3
Exam Tip
किसी वास्तविक (x) के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+9=0\) वास्तविक संख्या से संतुष्ट नहीं होता।
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Question 52/60
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
समीकरण \(x^2-2x+5=0\) का डिस्क्रिमिनेंट (D) क्या है?
What is the discriminant (D) of \(x^2-2x+5=0\)?
#roots
#discriminant
#no_real_roots
A (16)
B (0)
C (-16)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=4-20=-16\). Therefore there will be no real roots.
Step 2
Why this answer is correct
The correct answer is C. (-16). Here \(D=b^2-4ac=4-20=-16\). Therefore there will be no real roots.
Step 3
Exam Tip
यहां \(D=b^2-4ac=4-20=-16\) है। इसलिए वास्तविक मूल नहीं होंगे।
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Question 53/60
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
समीकरण \(x^2+4=0\) के वास्तविक मूलों की संख्या कितनी है?
How many real roots does \(x^2+4=0\) have?
#roots
#no_real_roots
#number_of_roots
A (2)
B (1)
C (0)
D (4)
Explanation opens after your attempt
Step 1
Concept
Because \(x^2\ge 0\) so \(x^2+4\) never becomes (0). Therefore it has no real root.
Step 2
Why this answer is correct
The correct answer is C. (0). Because \(x^2\ge 0\) so \(x^2+4\) never becomes (0). Therefore it has no real root.
Step 3
Exam Tip
क्योंकि \(x^2\ge 0\) होता है इसलिए \(x^2+4\) कभी (0) नहीं बनता। इसलिए कोई वास्तविक मूल नहीं है।
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Question 54/60
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
समीकरण \(x^2+1=0\) के वास्तविक मूलों के बारे में सही कथन कौन सा है?
Which statement is correct about the real roots of \(x^2+1=0\)?
#roots
#no_real_roots
#concept
A दो वास्तविक मूल हैं / It has two real roots
B एक वास्तविक मूल है / It has one real root
C कोई वास्तविक मूल नहीं है / It has no real roots
D मूल (1) और (-1) हैं / The roots are (1) and (-1)
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं है / It has no real roots
Step 1
Concept
\(x^2\) is never negative so \(x^2+1=0\) is not satisfied by any real number. Sign checking helps solve such questions quickly.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं है / It has no real roots. \(x^2\) is never negative so \(x^2+1=0\) is not satisfied by any real number. Sign checking helps solve such questions quickly.
Step 3
Exam Tip
\(x^2\) कभी ऋणात्मक नहीं होता इसलिए \(x^2+1=0\) वास्तविक संख्या से संतुष्ट नहीं होता। संकेत से ऐसे प्रश्न जल्दी हल होते हैं।
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Question 55/60
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+14x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+14x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>49)
B (k=49)
C (k<49)
D \(k\leq49\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).
Step 2
Why this answer is correct
The correct answer is A. (k>49). For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (196-4k<0), इसलिए (k>49)।
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Question 56/60
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+12x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+12x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>36)
B (k=36)
C (k<36)
D \(k\leq36\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).
Step 2
Why this answer is correct
The correct answer is A. (k>36). For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (144-4k<0), इसलिए (k>36)।
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Question 57/60
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2+10x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+10x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>25)
B (k=25)
C (k<25)
D \(k\leq25\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (100-4k<0), so (k>25).
Step 2
Why this answer is correct
The correct answer is A. (k>25). For no real roots, (D<0) is needed. Here (100-4k<0), so (k>25).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (100-4k<0), इसलिए (k>25)।
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Question 58/60
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+8x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+8x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#hard
A (k>16)
B (k=16)
C (k<16)
D \(k\leq16\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (64-4k<0), so (k>16).
Step 2
Why this answer is correct
The correct answer is A. (k>16). For no real roots, (D<0) is needed. Here (64-4k<0), so (k>16).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (64-4k<0), इसलिए (k>16)।
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Question 59/60
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+4x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+4x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#hard
A (k>4)
B (k=4)
C (k<4)
D \(k\leq4\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (16-4k<0), so (k>4).
Step 2
Why this answer is correct
The correct answer is A. (k>4). For no real roots, (D<0) is needed. Here (16-4k<0), so (k>4).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (16-4k<0), इसलिए (k>4)।
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Question 60/60
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी द्विघात समीकरण का विवेचक (D<0) है तो वास्तविक मूलों के बारे में क्या सही है?
If the discriminant (D<0), what is true about real roots?
#quadratic-equations
#discriminant
#no-real-roots
A दो समान वास्तविक मूल होते हैं / It has two equal real roots
B दो भिन्न वास्तविक मूल होते हैं / It has two distinct real roots
C कोई वास्तविक मूल नहीं होता / It has no real roots
D एक वास्तविक मूल होता है / It has one real root
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक मूल नहीं होता / It has no real roots
Step 1
Concept
When (D<0), there are no real roots. A negative discriminant gives no roots on the real number line.
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक मूल नहीं होता / It has no real roots. When (D<0), there are no real roots. A negative discriminant gives no roots on the real number line.
Step 3
Exam Tip
(D<0) होने पर वास्तविक मूल नहीं होते। विवेचक नकारात्मक हो तो वास्तविक संख्या रेखा पर मूल नहीं मिलते।
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