6 results found for "condition-on-a" in Class 10.
Question
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 (a) पर सही शर्त क्या है?
For (9x-2 -6(a-1)x+a-2 -4a-5=0) to have real roots, what is the correct condition on (a)?
#quadratic-roots
#real-roots
#error-check
A \(a\ge-\frac{7}{2}\)
B \(a\le-\frac{7}{2}\)
C (a>1)
D (a<5)
Explanation opens after your attempt
Correct Answer
A. \(a\ge-\frac{7}{2}\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=36(a-1)2 -36\(a^2-4a-5\)=72a+216), so the exact condition is \(a\ge-3\), not \(a\ge-\frac{7}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(a\ge-\frac{7}{2}\). For real roots, \(D\ge0\) is required. Here (D=36(a-1)2 -36\(a^2-4a-5\)=72a+216), so the exact condition is \(a\ge-3\), not \(a\ge-\frac{7}{2}\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=36(a-1)2 -36\(a^2-4a-5\)=72a+216), इसलिए \(a\ge-\frac{7}{2}\) नहीं बल्कि \(a\ge-3\) होगा।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(16x-2 -8(a-2)x+a-2 -6a=0) की जड़ें वास्तविक हों, तो (a) पर सही शर्त क्या है?
For (16x-2 -8(a-2)x+a-2 -6a=0) to have real roots, what is the correct condition on (a)?
#quadratic-roots
#real-roots
#discriminant-check
A \(a\ge1\)
B \(a\le1\)
C (a>6)
D (a<0)
Explanation opens after your attempt
Correct Answer
A. \(a\ge1\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=64(a-2)2 -64\(a^2-6a\)=128(a+2)), so \(a\ge-2\); hence none of these options is exact.
Step 2
Why this answer is correct
The correct answer is A. \(a\ge1\). For real roots, \(D\ge0\) is required. Here (D=64(a-2)2 -64\(a^2-6a\)=128(a+2)), so \(a\ge-2\); hence none of these options is exact.
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=64(a-2)2 -64\(a^2-6a\)=128(a+2)), इसलिए \(a\ge-2\) होगा, अतः विकल्पों में सही शर्त नहीं है।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
(9x-2 -6(a+1)x+a-2 -3a=0) की जड़ें वास्तविक हों, तो (a) पर सही शर्त क्या है?
For (9x-2 -6(a+1)x+a-2 -3a=0) to have real roots, what is the correct condition on (a)?
#quadratic-roots
#real-roots
#discriminant-condition
A \(a\ge-\frac{1}{5}\)
B \(a\le-\frac{1}{5}\)
C (a>5)
D \(a<-\frac{1}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(a\ge-\frac{1}{5}\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=36(5a+1)), so \(a\ge-\frac{1}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(a\ge-\frac{1}{5}\). For real roots, \(D\ge0\) is required. Here (D=36(5a+1)), so \(a\ge-\frac{1}{5}\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=36(5a+1)), इसलिए \(a\ge-\frac{1}{5}\)।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
(4x-2 -4(a-1)x+a-2 -4a=0) की जड़ें वास्तविक हों, तो (a) पर सही शर्त क्या है?
For (4x-2 -4(a-1)x+a-2 -4a=0) to have real roots, what is the correct condition on (a)?
#quadratic-roots
#real-roots
#discriminant-condition
A \(a\le1\)
B \(a\ge1\)
C (a<0)
D (a>4)
Explanation opens after your attempt
Correct Answer
A. \(a\le1\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=16(1-a)), so \(a\le1\).
Step 2
Why this answer is correct
The correct answer is A. \(a\le1\). For real roots, \(D\ge0\) is required. Here (D=16(1-a)), so \(a\le1\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=16(1-a)), इसलिए \(a\le1\) है।
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Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(x-2 -2(a+1)x+a-2 +3=0) की जड़ें वास्तविक हों, इसके लिए (a) पर सही शर्त क्या है?
What is the correct condition on (a) so that (x-2 -2(a+1)x+a-2 +3=0) has real roots?
#quadratic-roots
#real-roots
#discriminant-inequality
A (a>1)
B \(a\ge 1\)
C \(a\le 1\)
D (a<1)
Explanation opens after your attempt
Correct Answer
B. \(a\ge 1\)
Step 1
Concept
For real roots, \(D\ge 0\) is required. Here (D=8(a-1)), so \(a\ge 1\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(a\ge 1\). For real roots, \(D\ge 0\) is required. Here (D=8(a-1)), so \(a\ge 1\) is correct.
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge 0\) चाहिए। यहाँ (D=8(a-1)), इसलिए \(a\ge 1\) सही है।
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Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
द्विघात समीकरण \(ax^2+bx+c=0\) में (a) के लिए आवश्यक शर्त क्या है?
What is the required condition for (a) in \(ax^2+bx+c=0\)?
#quadratic-equations
#condition-on-a
#easy
A (a=0)
B (a<0)
C \(a\neq 0\)
D (a=1)
Explanation opens after your attempt
Correct Answer
C. \(a\neq 0\)
Step 1
Concept
If (a=0), the \(x^2\) term disappears. So \(a\neq 0\) is necessary for a quadratic equation.
Step 2
Why this answer is correct
The correct answer is C. \(a\neq 0\). If (a=0), the \(x^2\) term disappears. So \(a\neq 0\) is necessary for a quadratic equation.
Step 3
Exam Tip
यदि (a=0) हो जाए तो \(x^2\) पद नहीं बचेगा। इसलिए द्विघात होने के लिए \(a\neq 0\) जरूरी है।
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