Question 1/3
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (p(x)=x-2 -2\sqrt{5}x+5) है, तो इसके शून्यकों के बारे में सही कथन कौन सा है?
If (p(x)=x-2 -2\sqrt{5}x+5), which statement about its zeroes is correct?
#repeated-zero
#irrational-zero
#polynomial
A दोनों शून्यक \(\sqrt{5}\) हैं / Both zeroes are \(\sqrt{5}\)
B दोनों शून्यक \(-\sqrt{5}\) हैं / Both zeroes are \(-\sqrt{5}\)
C शून्यक \(\sqrt{5}\) और \(-\sqrt{5}\) हैं / Zeroes are \(\sqrt{5}\) and \(-\sqrt{5}\)
D कोई वास्तविक शून्यक नहीं है / No real zero exists
Explanation opens after your attempt
Correct Answer
A. दोनों शून्यक \(\sqrt{5}\) हैं / Both zeroes are \(\sqrt{5}\)
Step 1
Concept
This polynomial equals (\(x-\sqrt{5}\)2 ). Hence \(\sqrt{5}\) is a repeated zero.
Step 2
Why this answer is correct
The correct answer is A. दोनों शून्यक \(\sqrt{5}\) हैं / Both zeroes are \(\sqrt{5}\). This polynomial equals (\(x-\sqrt{5}\)2 ). Hence \(\sqrt{5}\) is a repeated zero.
Step 3
Exam Tip
यह बहुपद (\(x-\sqrt{5}\)2 ) के बराबर है। अतः \(\sqrt{5}\) दोहरा शून्यक है।
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Question 2/3
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
वह एकघात बहुपद कौन सा है जिसका शून्यक \(2\sqrt{3}\) है?
Which linear polynomial has zero \(2\sqrt{3}\)?
#linear-polynomial
#irrational-zero
#concept
A \(x-2\sqrt{3}\)
B \(x+2\sqrt{3}\)
C \(2x-\sqrt{3}\)
D \(x^2-12\)
Explanation opens after your attempt
Correct Answer
A. \(x-2\sqrt{3}\)
Step 1
Concept
A linear polynomial \(x-\alpha\) has zero \(\alpha\). Here \(\alpha=2\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(x-2\sqrt{3}\). A linear polynomial \(x-\alpha\) has zero \(\alpha\). Here \(\alpha=2\sqrt{3}\).
Step 3
Exam Tip
एकघात बहुपद \(x-\alpha\) का शून्यक \(\alpha\) होता है। यहाँ \(\alpha=2\sqrt{3}\) है।
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Question 3/3
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी ग्राफ में (x)-अक्ष से प्रतिच्छेद (\(-\sqrt{3},0\)) है तो शून्यक क्या है?
If a graph has (x)-axis intersection (\(-\sqrt{3},0\)), what is the zero?
#irrational-zero
#x-intercept
#graph
A \(-\sqrt{3}\)
B \(\sqrt{3}\)
C (0)
D (\(-\sqrt{3},0\))
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{3}\)
Step 1
Concept
A zero is the (x)-coordinate of the intercept. An irrational number can also be a zero.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{3}\). A zero is the (x)-coordinate of the intercept. An irrational number can also be a zero.
Step 3
Exam Tip
शून्यक प्रतिच्छेद का (x)-निर्देशांक होता है। अपरिमेय संख्या भी शून्यक हो सकती है।
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