Question 1/4
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि \(\alpha+\beta=10\) और \(\alpha\beta=21\), तो शून्यक कौन से होंगे?
If \(\alpha+\beta=10\) and \(\alpha\beta=21\), what will the zeroes be?
#sum-product
#zeroes
#rational-zeroes
A (7) और (3) / (7) and (3)
B \(5+\sqrt{5}\) और \(5-\sqrt{5}\) / \(5+\sqrt{5}\) and \(5-\sqrt{5}\)
C \(4+\sqrt{3}\) और \(4-\sqrt{3}\) / \(4+\sqrt{3}\) and \(4-\sqrt{3}\)
D \(6+\sqrt{2}\) और \(6-\sqrt{2}\) / \(6+\sqrt{2}\) and \(6-\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. (7) और (3) / (7) and (3)
Step 1
Concept
(7+3=10) and \(7\cdot3=21\). In exams do not choose only by seeing an irrational form.
Step 2
Why this answer is correct
The correct answer is A. (7) और (3) / (7) and (3). (7+3=10) and \(7\cdot3=21\). In exams do not choose only by seeing an irrational form.
Step 3
Exam Tip
(7+3=10) और \(7\cdot3=21\) है। परीक्षा में केवल अपरिमेय रूप देखकर उत्तर न चुनें।
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Question 2/4
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि (p(x)=x-2 -14x+45), तो शून्यकों का प्रकार क्या है?
If (p(x)=x-2 -14x+45), what is the type of its zeroes?
#discriminant
#rational-zeroes
#polynomials
A वास्तविक परिमेय / Real rational
B वास्तविक अपरिमेय / Real irrational
C समान वास्तविक / Equal real
D वास्तविक नहीं / Not real
Explanation opens after your attempt
Correct Answer
A. वास्तविक परिमेय / Real rational
Step 1
Concept
The discriminant is (196-180=16) and \(\sqrt{16}=4\) is rational. Hence the zeroes are real rational.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक परिमेय / Real rational. The discriminant is (196-180=16) and \(\sqrt{16}=4\) is rational. Hence the zeroes are real rational.
Step 3
Exam Tip
विविक्तकर (196-180=16) है और \(\sqrt{16}=4\) परिमेय है। इसलिए शून्यक वास्तविक परिमेय हैं।
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Question 3/4
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि (p(x)=x-2 -16) है, तो शून्यकों के प्रकार के बारे में सही कथन कौन सा है?
If (p(x)=x-2 -16), which statement about the type of zeroes is correct?
#real-numbers
#rational-zeroes
#common-mistake
A दोनों परिमेय वास्तविक हैं / Both are rational real
B दोनों अपरिमेय वास्तविक हैं / Both are irrational real
C दोनों अवास्तविक हैं / Both are non-real
D एक परिमेय और एक अपरिमेय है / One is rational and one is irrational
Explanation opens after your attempt
Correct Answer
A. दोनों परिमेय वास्तविक हैं / Both are rational real
Step 1
Concept
From \(x^2-16=0\), \(x=\pm4\), which are rational real. Not every square-root type question gives irrational roots.
Step 2
Why this answer is correct
The correct answer is A. दोनों परिमेय वास्तविक हैं / Both are rational real. From \(x^2-16=0\), \(x=\pm4\), which are rational real. Not every square-root type question gives irrational roots.
Step 3
Exam Tip
\(x^2-16=0\) से \(x=\pm4\), जो परिमेय वास्तविक हैं। हर वर्गमूल वाला प्रश्न अपरिमेय नहीं होता।
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Question 4/4
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि \(x^2-4x+r\) के शून्यक परिमेय हैं, तो (r=3) रखने पर कथन कैसा है?
If zeroes of \(x^2-4x+r\) are rational, what happens when (r=3)?
#rational-zeroes
#discriminant
#comparison
A कथन सही है / The statement is true
B कथन गलत है क्योंकि शून्यक अपरिमेय हैं / The statement is false because zeroes are irrational
C कथन गलत है क्योंकि (D<0) / The statement is false because (D<0)
D कथन गलत है क्योंकि शून्यक बराबर हैं / The statement is false because zeroes are equal
Explanation opens after your attempt
Correct Answer
A. कथन सही है / The statement is true
Step 1
Concept
For (r=3), (D=16-12=4), which is a perfect square. Therefore the zeroes are rational.
Step 2
Why this answer is correct
The correct answer is A. कथन सही है / The statement is true. For (r=3), (D=16-12=4), which is a perfect square. Therefore the zeroes are rational.
Step 3
Exam Tip
(r=3) पर (D=16-12=4) है, जो पूर्ण वर्ग है। इसलिए शून्यक परिमेय हैं।
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