6 results found for "zero_sum" in Class 10.
Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि मूलों का योग (0) और गुणनफल (-36) है तो मोनिक समीकरण कौन सा होगा?
If the sum of roots is (0) and product is (-36), which monic equation is formed?
#roots
#equation_from_sum_product
#zero_sum
A \(x^2-36=0\)
B \(x^2+36=0\)
C \(x^2-36x=0\)
D \(x^2+36x=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-36=0\)
Step 1
Concept
The monic equation is (x-2 -(0)x+(-36)=0). Therefore \(x^2-36=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-36=0\). The monic equation is (x-2 -(0)x+(-36)=0). Therefore \(x^2-36=0\) is correct.
Step 3
Exam Tip
मोनिक समीकरण (x-2 -(0)x+(-36)=0) होगा। इसलिए \(x^2-36=0\) सही है।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि किसी द्विघात समीकरण के मूलों का योग (0) है तो मूलों के बारे में सही कथन कौन सा हो सकता है?
If the sum of roots of a quadratic equation is (0), which statement about the roots can be correct?
#roots
#zero_sum
#reasoning
A मूल एक दूसरे के विपरीत हैं / The roots are opposites of each other
B दोनों मूल हमेशा (1) हैं / Both roots are always (1)
C दोनों मूल हमेशा धनात्मक हैं / Both roots are always positive
D मूलों का गुणनफल हमेशा (0) है / The product is always (0)
Explanation opens after your attempt
Correct Answer
A. मूल एक दूसरे के विपरीत हैं / The roots are opposites of each other
Step 1
Concept
If \(\alpha+\beta=0\), then \(\beta=-\alpha\). Therefore the roots can be opposites.
Step 2
Why this answer is correct
The correct answer is A. मूल एक दूसरे के विपरीत हैं / The roots are opposites of each other. If \(\alpha+\beta=0\), then \(\beta=-\alpha\). Therefore the roots can be opposites.
Step 3
Exam Tip
यदि \(\alpha+\beta=0\) है तो \(\beta=-\alpha\) होता है। इसलिए मूल विपरीत हो सकते हैं।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि मूलों का योग (0) और गुणनफल (-25) है तो मोनिक समीकरण कौन सा होगा?
If the sum of roots is (0) and product is (-25), which monic equation is formed?
#roots
#equation_from_sum_product
#zero_sum
A \(x^2-25=0\)
B \(x^2+25=0\)
C \(x^2-25x=0\)
D \(x^2+25x=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-25=0\)
Step 1
Concept
The monic equation is (x-2 -(0)x+(-25)=0). Therefore \(x^2-25=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-25=0\). The monic equation is (x-2 -(0)x+(-25)=0). Therefore \(x^2-25=0\) is correct.
Step 3
Exam Tip
मोनिक समीकरण (x-2 -(0)x+(-25)=0) होगा। इसलिए \(x^2-25=0\) सही है।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि मूलों का योग (0) और गुणनफल (-16) है तो मोनिक समीकरण कौन सा होगा?
If the sum of roots is (0) and product is (-16), which monic equation is formed?
#roots
#equation_from_sum_product
#zero_sum
A \(x^2-16=0\)
B \(x^2+16=0\)
C \(x^2-16x=0\)
D \(x^2+16x=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-16=0\)
Step 1
Concept
The monic equation is (x-2 -(0)x+(-16)=0). Therefore \(x^2-16=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-16=0\). The monic equation is (x-2 -(0)x+(-16)=0). Therefore \(x^2-16=0\) is correct.
Step 3
Exam Tip
मोनिक समीकरण (x-2 -(0)x+(-16)=0) होगा। इसलिए \(x^2-16=0\) सही है।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि (p(x)=x-2 -2x-2) का एक शून्यक \(1+\sqrt{3}\) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 -2x-2) is \(1+\sqrt{3}\), what is the other zero?
#other-zero
#sum-of-zeroes
#conjugate
A \(1-\sqrt{3}\)
B \(-1+\sqrt{3}\)
C \(1+\sqrt{3}\)
D \(-1-\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(1-\sqrt{3}\)
Step 1
Concept
The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 2
Why this answer is correct
The correct answer is A. \(1-\sqrt{3}\). The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 3
Exam Tip
शून्यकों का योग (2) है, इसलिए दूसरा शून्यक (2-\(1+\sqrt{3}\)=1-\sqrt{3}) है। परिमेय गुणांकों में संयुग्मी भी मिलता है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि \(\alpha=\sqrt{5}\) और \(\beta=-\sqrt{5}\) हैं, तो \(\alpha+\beta\) और \(\alpha\beta\) का सही युग्म कौन सा है?
If \(\alpha=\sqrt{5}\) and \(\beta=-\sqrt{5}\), which is the correct pair of \(\alpha+\beta\) and \(\alpha\beta\)?
#sum-product
#irrational
#real-numbers
A (0,-5)
B (0,5)
C \(2\sqrt{5},-5\)
D \(-2\sqrt{5},5\)
Explanation opens after your attempt
Step 1
Concept
(\sqrt{5}+\(-\sqrt{5}\)=0) and (\sqrt{5}\cdot\(-\sqrt{5}\)=-5). Opposite irrationals can have zero sum.
Step 2
Why this answer is correct
The correct answer is A. (0,-5). (\sqrt{5}+\(-\sqrt{5}\)=0) and (\sqrt{5}\cdot\(-\sqrt{5}\)=-5). Opposite irrationals can have zero sum.
Step 3
Exam Tip
(\sqrt{5}+\(-\sqrt{5}\)=0) और (\sqrt{5}\cdot\(-\sqrt{5}\)=-5) है। विपरीत अपरिमेयों का योग शून्य हो सकता है।
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