Question 1/6
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-5x+6=0\) के मूलों की प्रकृति क्या है?
What is the nature of roots of the equation \(x^2-5x+6=0\)?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और असमान/two real and distinct
Step 1
Concept
Here (D=(-5)2-4(1)(6)=1>0). So the roots are real and distinct.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और असमान / two real and distinct. Here (D=(-5)2-4(1)(6)=1>0). So the roots are real and distinct.
Step 3
Exam Tip
यहां (D=(-5)2-4(1)(6)=1>0) है। इसलिए मूल वास्तविक और असमान हैं।
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Question 2/6
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-20x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-20x+k=0\) are real and distinct, what is the correct condition on (k)?
Explanation opens after your attempt
Correct Answer
A. (k<100)
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 2
Why this answer is correct
The correct answer is A. (k<100). For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (400-4k>0), इसलिए (k<100)।
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Question 3/6
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2-16x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-16x+k=0\) are real and distinct, what is the correct condition on (k)?
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (256-4k>0), so (k<64).
Step 2
Why this answer is correct
The correct answer is A. (k<64). For real and distinct roots, (D>0) is needed. Here (256-4k>0), so (k<64).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (256-4k>0), इसलिए (k<64)।
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Question 4/6
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2-12x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-12x+k=0\) are real and distinct, what is the correct condition on (k)?
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).
Step 2
Why this answer is correct
The correct answer is A. (k<36). For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (144-4k>0), इसलिए (k<36)।
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Question 5/6
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-8x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-8x+k=0\) are real and distinct, what is the correct condition on (k)?
Explanation opens after your attempt
Step 1
Concept
For real and distinct 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 real and distinct roots, (D>0) is needed. Here (64-4k>0), so (k<16).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (64-4k>0), इसलिए (k<16)।
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Question 6/6
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2-6x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-6x+k=0\) are real and distinct, what is the correct condition on (k)?
Explanation opens after your attempt
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (36-4k>0), so (k<9).
Step 2
Why this answer is correct
The correct answer is A. (k<9). For real and distinct roots, (D>0) is needed. Here (36-4k>0), so (k<9).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (36-4k>0), इसलिए (k<9)।
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