Question 1/9
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(9x-2 -6(a-1)x+a-2 -4a-5=0) की जड़ें वास्तविक हों, तो सही शर्त क्या है?
What is the correct condition for (9x-2 -6(a-1)x+a-2 -4a-5=0) to have real roots?
#quadratic-roots
#real-roots
#parameter-condition
A \(a\ge-3\)
B \(a\le-3\)
C (a>3)
D (a< -3)
Explanation opens after your attempt
Correct Answer
A. \(a\ge-3\)
Step 1
Concept
Here (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)). For real roots, \(D\ge0\), so \(a\ge-3\).
Step 2
Why this answer is correct
The correct answer is A. \(a\ge-3\). Here (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)). For real roots, \(D\ge0\), so \(a\ge-3\).
Step 3
Exam Tip
यहाँ (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)) है। वास्तविक जड़ों के लिए \(D\ge0\), इसलिए \(a\ge-3\)।
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Question 2/9
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि ((m-1 )x-2 +2(m+1)x+(m-1 )=0) की जड़ें वास्तविक और व्युत्क्रम हों, तो (m) पर सही शर्त क्या है?
If ((m-1 )x-2 +2(m+1)x+(m-1 )=0) has real reciprocal roots, what is the correct condition on (m)?
#quadratic-roots
#reciprocal-roots
#parameter-condition
A \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\)
B (m<0)
C (m=1)
D \(m\le0\)
Explanation opens after your attempt
Correct Answer
A. \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\)
Step 1
Concept
The product of roots is \(\frac{m-1}{m-1}=1\), so \(m\neq1\) is needed. For real roots, \(D=16m\ge0\), hence \(m\ge0\) and \(m\neq1\).
Step 2
Why this answer is correct
The correct answer is A. \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\). The product of roots is \(\frac{m-1}{m-1}=1\), so \(m\neq1\) is needed. For real roots, \(D=16m\ge0\), hence \(m\ge0\) and \(m\neq1\).
Step 3
Exam Tip
जड़ों का गुणनफल \(\frac{m-1}{m-1}=1\) है, इसलिए \(m\neq1\) चाहिए। वास्तविक जड़ों के लिए \(D=16m\ge0\), अतः \(m\ge0\) और \(m\neq1\)।
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Question 3/9
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि (x-2 -2mx+\(m^2-m\)=0) की जड़ें वास्तविक हों, तो (m) पर सही शर्त क्या है?
If (x-2 -2mx+\(m^2-m\)=0) has real roots, what is the correct condition on (m)?
#quadratic-roots
#real-roots
#parameter-condition
A (m>0)
B (m<0)
C \(m\ge0\)
D \(m\le0\)
Explanation opens after your attempt
Correct Answer
C. \(m\ge0\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=4m), so \(m\ge0\).
Step 2
Why this answer is correct
The correct answer is C. \(m\ge0\). For real roots, \(D\ge0\) is required. Here (D=4m), so \(m\ge0\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=4m), इसलिए \(m\ge0\)।
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Question 4/9
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
\(kx^2+6x+9=0\) की वास्तविक जड़ें हों और \(k\ne0\), तो (k) पर सही शर्त कौन-सी है?
For \(kx^2+6x+9=0\) to have real roots with \(k\ne0\), which condition on (k) is correct?
#quadratic-roots
#real-roots
#parameter-condition
A \(k\le 1,\ k\ne0\)
B (k>1)
C \(k\ge 1\)
D (k<0) केवल / (k<0) only
Explanation opens after your attempt
Correct Answer
A. \(k\le 1,\ k\ne0\)
Step 1
Concept
For real roots, \(D=36-36k\ge0\) is required. Thus \(k\le1\), and \(k\ne0\) is also needed for a quadratic equation.
Step 2
Why this answer is correct
The correct answer is A. \(k\le 1,\ k\ne0\). For real roots, \(D=36-36k\ge0\) is required. Thus \(k\le1\), and \(k\ne0\) is also needed for a quadratic equation.
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D=36-36k\ge0\) होना चाहिए। इसलिए \(k\le1\) और द्विघात के लिए \(k\ne0\) भी जरूरी है।
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Question 5/9
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 6/9
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 7/9
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
समीकरण \(x^2+6x+k=0\) के वास्तविक मूल होने के लिए (k) के बारे में कौन सी शर्त सही है?
For \(x^2+6x+k=0\) to have real roots, which condition on (k) is correct?
#roots
#real_roots
#parameter_condition
A \(k\le9\)
B (k>9)
C (k=12)
D (k<0) ही होगा / Only (k<0)
Explanation opens after your attempt
Correct Answer
A. \(k\le9\)
Step 1
Concept
For real roots \(D\ge0\) is required. From \(36-4k\ge0\), we get \(k\le9\).
Step 2
Why this answer is correct
The correct answer is A. \(k\le9\). For real roots \(D\ge0\) is required. From \(36-4k\ge0\), we get \(k\le9\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। \(36-4k\ge0\) से \(k\le9\) मिलता है।
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Question 8/9
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
समीकरण \(x^2+4x+k=0\) के वास्तविक मूल होने के लिए (k) के बारे में कौन सी शर्त सही है?
For \(x^2+4x+k=0\) to have real roots, which condition on (k) is correct?
#roots
#real_roots
#parameter_condition
A \(k\le4\)
B (k>4)
C (k=8)
D (k<0) ही होगा / Only (k<0)
Explanation opens after your attempt
Correct Answer
A. \(k\le4\)
Step 1
Concept
For real roots \(D\ge0\) is required. From \(16-4k\ge0\), we get \(k\le4\).
Step 2
Why this answer is correct
The correct answer is A. \(k\le4\). For real roots \(D\ge0\) is required. From \(16-4k\ge0\), we get \(k\le4\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। \(16-4k\ge0\) से \(k\le4\) मिलता है।
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Question 9/9
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
समीकरण \(x^2+2x+k=0\) के वास्तविक मूल होने के लिए (k) के बारे में कौन सी शर्त सही है?
For \(x^2+2x+k=0\) to have real roots, which condition on (k) is correct?
#roots
#real_roots
#parameter_condition
A \(k\le1\)
B (k>1)
C (k=2)
D (k<0) ही होगा / Only (k<0)
Explanation opens after your attempt
Correct Answer
A. \(k\le1\)
Step 1
Concept
For real roots \(D\ge0\) is required. From \(4-4k\ge0\), we get \(k\le1\).
Step 2
Why this answer is correct
The correct answer is A. \(k\le1\). For real roots \(D\ge0\) is required. From \(4-4k\ge0\), we get \(k\le1\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। \(4-4k\ge0\) से \(k\le1\) मिलता है।
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