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always real roots MCQ Questions for Class 10

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2 questions tagged with always real roots.

Question 1/2 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (5x^-2-2(k+1)x+(k-3)=0) के वास्तविक मूलों के लिए सही शर्त क्या है?

What is the correct condition for real roots of (5x^-2-2(k+1)x+(k-3)=0)?

Explanation opens after your attempt

Correct Answer

A. \(k^2-3k+16\ge0\)

Step 1

Concept

Here (D=4[(k+1)²-5(k-3)]=4\(k^2-3k+16\)). This expression is always positive, so real roots always exist.

Step 2

Why this answer is correct

The correct answer is A. \(k^2-3k+16\ge0\). Here (D=4[(k+1)²-5(k-3)]=4\(k^2-3k+16\)). This expression is always positive, so real roots always exist.

Step 3

Exam Tip

यहाँ (D=4[(k+1)²-5(k-3)]=4\(k^2-3k+16\)) है। यह अभिव्यक्ति हमेशा धनात्मक है, इसलिए वास्तविक मूल हमेशा मिलेंगे।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Hard
Level: 38

Question Hindi:
समीकरण (5x^2-2(k+1)x+(k-3)=0) के वास्तविक मूलों के लिए सही शर्त क्या है?

Question English:
What is the correct condition for real roots of (5x^2-2(k+1)x+(k-3)=0)?

Options:
A. (k^2-3k+16\ge0)
B. (k^2-3k+16<0)
C. (k=3) केवल / (k=3) only
D. कोई वास्तविक (k) नहीं / No real (k)

Correct Answer:
A. (k^2-3k+16\ge0)

Explanation Hindi:
यहाँ (D=4[(k+1)^2-5(k-3)]=4(k^2-3k+16)) है। यह अभिव्यक्ति हमेशा धनात्मक है, इसलिए वास्तविक मूल हमेशा मिलेंगे।

Explanation English:
Here (D=4[(k+1)^2-5(k-3)]=4(k^2-3k+16)). This expression is always positive, so real roots always exist.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
- Final narration script.
- Scene-by-scene visual direction.
- Text overlays for 16:9 and 9:16.
- Thumbnail idea.
- Hashtags: #MuftShiksha #FreeEducation #MCQ #Quiz #Class10 #Study

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Question 2/2 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण (2x^-2-(3q+1)x+q=0) के मूल हमेशा वास्तविक और भिन्न क्यों हैं?

Why are the roots of (2x^-2-(3q+1)x+q=0) always real and distinct?

Explanation opens after your attempt

Correct Answer

A. क्योंकि \(D=9q^2-2q+1>0\)Because \(D=9q^2-2q+1>0\)

Step 1

Concept

Here (D=(3q+1)²-8q=9q^-2-2q+1). Its own discriminant ((-2)²-4(9)(1)<0), so it is always positive.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि \(D=9q^2-2q+1>0\) / Because \(D=9q^2-2q+1>0\). Here (D=(3q+1)²-8q=9q^-2-2q+1). Its own discriminant ((-2)²-4(9)(1)<0), so it is always positive.

Step 3

Exam Tip

यहाँ (D=(3q+1)²-8q=9q^-2-2q+1) है। इसका अपना विविक्तकर ((-2)²-4(9)(1)<0) और मान सदैव धनात्मक है।

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AI Video Prompt 16:9 + 9:16

Is question ka premium MCQ video banane ke liye ready prompt. Copy karke Sora, Runway, Canva AI, CapCut AI, ChatGPT video workflow ya editor me use karein.

Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

Brand:
- Name: Muft Shiksha
- Website: https://muftshiksha.com
- Style: dark navy futuristic learning game UI, neon cyan/blue glow, gold reward highlights, clean Devanagari text, premium educational look.
- Do not add wrong facts. Do not change the question, options or answer.

Question Page:
https://muftshiksha.com/question/why-are-the-roots-of-2x-2-3q-1-x-q-0-always-real-and-distinct

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Hard
Level: 37

Question Hindi:
समीकरण (2x^2-(3q+1)x+q=0) के मूल हमेशा वास्तविक और भिन्न क्यों हैं?

Question English:
Why are the roots of (2x^2-(3q+1)x+q=0) always real and distinct?

Options:
A. क्योंकि (D=9q^2-2q+1>0) / Because (D=9q^2-2q+1>0)
B. क्योंकि (D=0) / Because (D=0)
C. क्योंकि (D<0) / Because (D<0)
D. क्योंकि (a=0) / Because (a=0)

Correct Answer:
A. क्योंकि (D=9q^2-2q+1>0) / Because (D=9q^2-2q+1>0)

Explanation Hindi:
यहाँ (D=(3q+1)^2-8q=9q^2-2q+1) है। इसका अपना विविक्तकर ((-2)^2-4(9)(1)<0) और मान सदैव धनात्मक है।

Explanation English:
Here (D=(3q+1)^2-8q=9q^2-2q+1). Its own discriminant ((-2)^2-4(9)(1)<0), so it is always positive.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
- Final narration script.
- Scene-by-scene visual direction.
- Text overlays for 16:9 and 9:16.
- Thumbnail idea.
- Hashtags: #MuftShiksha #FreeEducation #MCQ #Quiz #Class10 #Study

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always real roots MCQ Questions for Class 10

Practice Questions

समीकरण (5x^-2-2(k+1)x+(k-3)=0) के वास्तविक मूलों के लिए सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण (2x^-2-(3q+1)x+q=0) के मूल हमेशा वास्तविक और भिन्न क्यों हैं?

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always real roots MCQ Questions for Class 10

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समीकरण (5x-2-2(k+1)x+(k-3)=0) के वास्तविक मूलों के लिए सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण (2x-2-(3q+1)x+q=0) के मूल हमेशा वास्तविक और भिन्न क्यों हैं?

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समीकरण (5x^-2-2(k+1)x+(k-3)=0) के वास्तविक मूलों के लिए सही शर्त क्या है?

समीकरण (2x^-2-(3q+1)x+q=0) के मूल हमेशा वास्तविक और भिन्न क्यों हैं?