30 results found for "monic-quadratic" in Class 10.
Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x=3) और (x=8) किसी मोनिक द्विघात समीकरण के मूल हैं तो (x) का गुणांक क्या होगा?
If (x=3) and (x=8) are roots of a monic quadratic equation, what will be the coefficient of (x)?
#roots
#coefficient_from_roots
#monic
A (-11)
B (11)
C (24)
D (-24)
Explanation opens after your attempt
Step 1
Concept
\(The sum of roots is (3+8=11). In a monic equation the coefficient of (x) is (-(\)sum\()=-11).\)
Step 2
Why this answer is correct
\(The correct answer is A. (-11). The sum of roots is (3+8=11). In a monic equation the coefficient of (x) is (-(\)sum\()=-11).\)
Step 3
Exam Tip
मूलों का योग (3+8=11) है। मोनिक समीकरण में (x) का गुणांक (-(योग\()=-11) होता है\)।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि मूलों का योग (11) और गुणनफल (28) है तो मोनिक द्विघात समीकरण कौन सा होगा?
If the sum of roots is (11) and product is (28), which monic quadratic equation is formed?
#roots
#equation_from_sum_product
#monic
A \(x^2-11x+28=0\)
B \(x^2+11x+28=0\)
C \(x^2-28x+11=0\)
D \(x^2+28x+11=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-11x+28=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-11x+28=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-11x+28=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-11x+28=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-11x+28=0) सही है\)।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि (x=2) और (x=7) किसी मोनिक द्विघात समीकरण के मूल हैं तो (x) का गुणांक क्या होगा?
If (x=2) and (x=7) are roots of a monic quadratic equation, what will be the coefficient of (x)?
#roots
#coefficient_from_roots
#monic
A (-9)
B (9)
C (14)
D (-14)
Explanation opens after your attempt
Step 1
Concept
\(The sum of roots is (2+7=9). In a monic equation the coefficient of (x) is (-(\)sum\()=-9).\)
Step 2
Why this answer is correct
\(The correct answer is A. (-9). The sum of roots is (2+7=9). In a monic equation the coefficient of (x) is (-(\)sum\()=-9).\)
Step 3
Exam Tip
मूलों का योग (2+7=9) है। मोनिक समीकरण में (x) का गुणांक (-(योग\()=-9) होता है\)।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि मूलों का योग (9) और गुणनफल (18) है तो मोनिक द्विघात समीकरण कौन सा होगा?
If the sum of roots is (9) and product is (18), which monic quadratic equation is formed?
#roots
#equation_from_sum_product
#monic
A \(x^2-9x+18=0\)
B \(x^2+9x+18=0\)
C \(x^2-18x+9=0\)
D \(x^2+18x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-9x+18=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-9x+18=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-9x+18=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-9x+18=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-9x+18=0) सही है\)।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि (x=1) और (x=4) किसी मोनिक द्विघात समीकरण के मूल हैं तो (x) का गुणांक क्या होगा?
If (x=1) and (x=4) are roots of a monic quadratic equation, what will be the coefficient of (x)?
#roots
#coefficient_from_roots
#monic
A (-5)
B (5)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
\(The sum of roots is (1+4=5). In a monic equation the coefficient of (x) is (-(\)sum\()=-5).\)
Step 2
Why this answer is correct
\(The correct answer is A. (-5). The sum of roots is (1+4=5). In a monic equation the coefficient of (x) is (-(\)sum\()=-5).\)
Step 3
Exam Tip
मूलों का योग (1+4=5) है। मोनिक समीकरण में (x) का गुणांक (-(योग\()=-5) होता है\)।
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Question
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि मूलों का योग (7) और गुणनफल (10) है तो मोनिक द्विघात समीकरण कौन सा होगा?
If the sum of roots is (7) and product is (10), which monic quadratic equation is formed?
#roots
#equation_from_sum_product
#monic
A \(x^2-7x+10=0\)
B \(x^2+7x+10=0\)
C \(x^2-10x+7=0\)
D \(x^2+10x+7=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x+10=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-7x+10=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-7x+10=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-7x+10=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-7x+10=0) सही है\)।
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Question
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (5) और (5) हैं तो समीकरण कौन सा है?
If both roots of a monic quadratic equation are (5) and (5), which equation is it?
#roots
#equal_roots
#equation_from_roots
A \(x^2-10x+25=0\)
B \(x^2+10x+25=0\)
C \(x^2-5x+25=0\)
D \(x^2+5x-25=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+25=0\)
Step 1
Concept
If both roots are (5), the equation is ((x-5)2 =0). Expanding it gives \(x^2-10x+25=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+25=0\). If both roots are (5), the equation is ((x-5)2 =0). Expanding it gives \(x^2-10x+25=0\).
Step 3
Exam Tip
दोनों मूल (5) हों तो समीकरण ((x-5)2 =0) होगा। इसे खोलने पर \(x^2-10x+25=0\) मिलता है।
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Question
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
जिस मोनिक द्विघात समीकरण के मूलों का योग (10) और गुणनफल (21) है वह कौन सा है?
Which monic quadratic equation has sum of roots (10) and product of roots (21)?
#roots
#equation_from_sum_product
#monic
A \(x^2+10x+21=0\)
B \(x^2-10x+21=0\)
C \(x^2-21x+10=0\)
D \(x^2+21x+10=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-10x+21=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-10x+21=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is B. (x^2-10x+21=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-10x+21=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-10x+21=0) सही है\)।
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Question
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (-4) और (-4) हैं तो समीकरण कौन सा है?
If both roots of a monic quadratic equation are (-4) and (-4), which equation is it?
#roots
#equal_roots
#equation_from_roots
A \(x^2+8x+16=0\)
B \(x^2-8x+16=0\)
C \(x^2+4x+16=0\)
D \(x^2-4x-16=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+8x+16=0\)
Step 1
Concept
If both roots are (-4), the equation is ((x+4)2 =0). Expanding it gives \(x^2+8x+16=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+8x+16=0\). If both roots are (-4), the equation is ((x+4)2 =0). Expanding it gives \(x^2+8x+16=0\).
Step 3
Exam Tip
दोनों मूल (-4) हों तो समीकरण ((x+4)2 =0) होगा। इसे खोलने पर \(x^2+8x+16=0\) मिलता है।
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Question
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
जिस मोनिक द्विघात समीकरण के मूलों का योग (-9) और गुणनफल (20) है वह कौन सा है?
Which monic quadratic equation has sum of roots (-9) and product of roots (20)?
#roots
#equation_from_sum_product
#monic
A \(x^2+9x+20=0\)
B \(x^2-9x+20=0\)
C \(x^2+20x+9=0\)
D \(x^2-20x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+9x+20=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2+9x+20=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+9x+20=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2+9x+20=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2+9x+20=0) सही है\)।
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Question
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (7) और (7) हैं तो समीकरण कौन सा है?
If both roots of a monic quadratic equation are (7) and (7) then which equation is it?
#roots
#equal_roots
#equation_from_roots
A \(x^2-14x+49=0\)
B \(x^2+14x+49=0\)
C \(x^2-7x+49=0\)
D \(x^2+7x-49=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-14x+49=0\)
Step 1
Concept
With both roots (7) we get ((x-7)2 =0) which is \(x^2-14x+49=0\). Form a perfect square from repeated roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-14x+49=0\). With both roots (7) we get ((x-7)2 =0) which is \(x^2-14x+49=0\). Form a perfect square from repeated roots.
Step 3
Exam Tip
दोनों मूल (7) होने पर ((x-7)2 =0) मिलता है जो \(x^2-14x+49=0\) है। दोहराए मूल से पूर्ण वर्ग बनाएं।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी मोनिक द्विघात समीकरण के मूल (3r) और (4r) हैं तथा उनका योग (28) है, तो उस समीकरण का स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (3r) and (4r), and their sum is (28), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#expert
A (192)
B (28)
C (112)
D (84)
Explanation opens after your attempt
Step 1
Concept
From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).
Step 2
Why this answer is correct
The correct answer is A. (192). From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).
Step 3
Exam Tip
(3r+4r=28) से (r=4) मिलता है, इसलिए मूल (12) और (16) हैं। स्थिर पद मूलों का गुणनफल (192) होगा।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
मूलों का योग (-15) और गुणनफल (56) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-15) and product (56)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2+15x+56=0\)
B \(x^2-15x+56=0\)
C \(x^2+56x+15=0\)
D \(x^2-56x+15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+15x+56=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+15x+56=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-15) रखने पर (x^2+15x+56=0) मिलता है\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि किसी मोनिक द्विघात समीकरण के मूल (2r) और (5r) हैं तथा उनका योग (21) है, तो उस समीकरण का स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (2r) and (5r), and their sum is (21), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#expert
A (90)
B (21)
C (45)
D (63)
Explanation opens after your attempt
Step 1
Concept
From (2r+5r=21), we get (r=3), so the roots are (6) and (15). The constant term is the product of roots (90).
Step 2
Why this answer is correct
The correct answer is A. (90). From (2r+5r=21), we get (r=3), so the roots are (6) and (15). The constant term is the product of roots (90).
Step 3
Exam Tip
(2r+5r=21) से (r=3) मिलता है, इसलिए मूल (6) और (15) हैं। स्थिर पद मूलों का गुणनफल (90) होगा।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
मूलों का योग (-13) और गुणनफल (42) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-13) and product (42)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2+13x+42=0\)
B \(x^2-13x+42=0\)
C \(x^2+42x+13=0\)
D \(x^2-42x+13=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+13x+42=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-13) gives (x^2+13x+42=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+13x+42=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-13) gives (x^2+13x+42=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-13) रखने पर (x^2+13x+42=0) मिलता है\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि किसी मोनिक द्विघात समीकरण के मूल (r) और (3r) हैं तथा उनका योग (16) है, तो उस समीकरण का स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (r) and (3r), and their sum is (16), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#expert
A (48)
B (16)
C (64)
D (32)
Explanation opens after your attempt
Step 1
Concept
From (r+3r=16), we get (r=4), so the roots are (4) and (12). The constant term is the product of roots (48).
Step 2
Why this answer is correct
The correct answer is A. (48). From (r+3r=16), we get (r=4), so the roots are (4) and (12). The constant term is the product of roots (48).
Step 3
Exam Tip
(r+3r=16) से (r=4) मिलता है, इसलिए मूल (4) और (12) हैं। स्थिर पद मूलों का गुणनफल (48) होगा।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
मूलों का योग (-11) और गुणनफल (30) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-11) and product (30)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2+11x+30=0\)
B \(x^2-11x+30=0\)
C \(x^2+30x+11=0\)
D \(x^2-30x+11=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+11x+30=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-11) gives (x^2+11x+30=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+11x+30=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-11) gives (x^2+11x+30=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-11) रखने पर (x^2+11x+30=0) मिलता है\)।
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Question
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी मोनिक द्विघात समीकरण के मूल (r) और (2r) हैं तथा उनका योग (9) है, तो उस समीकरण में स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (r) and (2r), and their sum is (9), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#hard
A (18)
B (9)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
From (r+2r=9), we get (r=3), so the roots are (3) and (6). The constant term will be the product of roots (18).
Step 2
Why this answer is correct
The correct answer is A. (18). From (r+2r=9), we get (r=3), so the roots are (3) and (6). The constant term will be the product of roots (18).
Step 3
Exam Tip
(r+2r=9) से (r=3) मिलता है, इसलिए मूल (3) और (6) हैं। स्थिर पद मूलों का गुणनफल (18) होगा।
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Question
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
मूलों का योग (-9) और गुणनफल (20) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-9) and product (20)?
#quadratic-equations
#sum-product
#forming-equation
#hard
A \(x^2+9x+20=0\)
B \(x^2-9x+20=0\)
C \(x^2+20x+9=0\)
D \(x^2-20x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+9x+20=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-9) gives (x^2+9x+20=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+9x+20=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-9) gives (x^2+9x+20=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-9) रखने पर (x^2+9x+20=0) मिलता है\)।
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Question
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
मूलों का योग (7) और गुणनफल (10) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (7) and product (10)?
#quadratic-equations
#sum-product
#forming-equation
#hard
A \(x^2-7x+10=0\)
B \(x^2+7x+10=0\)
C \(x^2-10x+7=0\)
D \(x^2+10x-7=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x+10=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-7x+10=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-7x+10=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-7x+10=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-7x+10=0) सही है\)।
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Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि मूल (-5) और (4) हैं, तो मोनिक द्विघात समीकरण कौन-सा होगा?
If the roots are (-5) and (4), what will be the monic quadratic equation?
#quadratic-equations
#monic
#roots
#medium
A \(x^2+x-20=0\)
B \(x^2-x-20=0\)
C \(x^2+9x+20=0\)
D \(x^2-9x+20=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-20=0\)
Step 1
Concept
The factors are ((x+5)) and ((x-4)). Multiplying them gives \(x^2+x-20=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-20=0\). The factors are ((x+5)) and ((x-4)). Multiplying them gives \(x^2+x-20=0\).
Step 3
Exam Tip
गुणनखंड ((x+5)) और ((x-4)) होंगे। इन्हें गुणा करने पर \(x^2+x-20=0\) मिलता है।
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Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि मूल (-4) और (3) हैं, तो मोनिक द्विघात समीकरण कौन-सा होगा?
If the roots are (-4) and (3), what will be the monic quadratic equation?
#quadratic-equations
#monic
#roots
#medium
A \(x^2+x-12=0\)
B \(x^2-x-12=0\)
C \(x^2+7x+12=0\)
D \(x^2-7x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-12=0\)
Step 1
Concept
The factors will be ((x+4)) and ((x-3)). These give \(x^2+x-12=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-12=0\). The factors will be ((x+4)) and ((x-3)). These give \(x^2+x-12=0\).
Step 3
Exam Tip
गुणनखंड ((x+4)) और ((x-3)) होंगे। इनसे \(x^2+x-12=0\) मिलता है।
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Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि मूल (-2) और (5) हैं, तो मोनिक द्विघात समीकरण कौन-सा होगा?
If the roots are (-2) and (5), what will be the monic quadratic equation?
#quadratic-equations
#monic
#roots
#medium
A \(x^2-3x-10=0\)
B \(x^2+3x-10=0\)
C \(x^2-7x+10=0\)
D \(x^2+7x+10=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-10=0\)
Step 1
Concept
The factors are ((x+2)) and ((x-5)), giving \(x^2-3x-10=0\). Make factors with signs opposite to the roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-10=0\). The factors are ((x+2)) and ((x-5)), giving \(x^2-3x-10=0\). Make factors with signs opposite to the roots.
Step 3
Exam Tip
गुणनखंड ((x+2)) और ((x-5)) होंगे, जिनसे \(x^2-3x-10=0\) मिलता है। मूल के विपरीत चिन्ह वाले गुणनखंड बनाएं।
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Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
निम्न में से मोनिक द्विघात समीकरण कौन-सा है?
Which of the following is a monic quadratic equation?
#quadratic-equations
#monic-quadratic
#easy
A \(x^2+5x+6=0\)
B \(2x^2+x+1=0\)
C \(-3x^2+x=0\)
D \(4x^2-1=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x+6=0\)
Step 1
Concept
In a monic quadratic equation, the coefficient of \(x^2\) is (1). So \(x^2+5x+6=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x+6=0\). In a monic quadratic equation, the coefficient of \(x^2\) is (1). So \(x^2+5x+6=0\) is correct.
Step 3
Exam Tip
मोनिक द्विघात में \(x^2\) का गुणांक (1) होता है। इसलिए \(x^2+5x+6=0\) सही है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 28
शून्यकों \(2+\sqrt{6}\) और \(2-\sqrt{6}\) वाला एक मानक द्विघात बहुपद कौन सा है?
Which monic quadratic polynomial has zeroes \(2+\sqrt{6}\) and \(2-\sqrt{6}\)?
#forming polynomial
#irrational zeroes
#quadratic
A \(x^2-4x-2\)
B \(x^2+4x-2\)
C \(x^2-2x+4\)
D \(x^2-4x+10\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x-2\)
Step 1
Concept
The sum is (4) and the product is (4-6=-2), so the polynomial is \(x^2-4x-2\). Remember the formula \(x^2-Sx+P\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x-2\). The sum is (4) and the product is (4-6=-2), so the polynomial is \(x^2-4x-2\). Remember the formula \(x^2-Sx+P\).
Step 3
Exam Tip
योग (4) और गुणनफल (4-6=-2) है, इसलिए बहुपद \(x^2-4x-2\) है। परीक्षा में \(x^2-Sx+P\) सूत्र याद रखें।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि किसी एकक द्विघात बहुपद के शून्यक \(a+\sqrt{b}\) और \(a-\sqrt{b}\) हैं, तो उसके विविक्तकर का मान क्या होगा?
If the zeroes of a monic quadratic polynomial are \(a+\sqrt{b}\) and \(a-\sqrt{b}\), what will be its discriminant?
#general-discriminant
#conjugates
#expert
A (4b)
B (b)
C (2b)
D \(a^2-b\)
Explanation opens after your attempt
Step 1
Concept
The polynomial is (x-2 -2ax+\(a^2-b\)). Its discriminant is (4a-2 -4\(a^2-b\)=4b).
Step 2
Why this answer is correct
The correct answer is A. (4b). The polynomial is (x-2 -2ax+\(a^2-b\)). Its discriminant is (4a-2 -4\(a^2-b\)=4b).
Step 3
Exam Tip
बहुपद (x-2 -2ax+\(a^2-b\)) होगा। इसका विविक्तकर (4a-2 -4\(a^2-b\)=4b) है।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि \(\sqrt{3}\) और \(\sqrt{12}\) किसी द्विघात बहुपद के शून्यक हैं, तो एकक बहुपद में (x) का गुणांक क्या होगा?
If \(\sqrt{3}\) and \(\sqrt{12}\) are zeroes of a monic quadratic polynomial, what will be the coefficient of (x)?
#radical-simplification
#monic-polynomial
#coefficient
A \(-3\sqrt{3}\)
B \(-\sqrt{15}\)
C \(3\sqrt{3}\)
D \(-2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-3\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.
Step 2
Why this answer is correct
The correct answer is A. \(-3\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\), इसलिए योग \(3\sqrt{3}\) है। एकक बहुपद में (x) का गुणांक शून्यकों के योग का ऋणात्मक होता है।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि किसी एकक द्विघात बहुपद के शून्यक \(4+\sqrt{11}\) और \(4-\sqrt{11}\) हैं, तो स्थिर पद क्या होगा?
If the zeroes of a monic quadratic polynomial are \(4+\sqrt{11}\) and \(4-\sqrt{11}\), what will be the constant term?
#conjugate-zeroes
#constant-term
#quadratic
A (5)
B (27)
C (8)
D \(16+\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
The constant term is the product, and (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5). In conjugate products, the irrational middle part cancels.
Step 2
Why this answer is correct
The correct answer is A. (5). The constant term is the product, and (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5). In conjugate products, the irrational middle part cancels.
Step 3
Exam Tip
स्थिर पद गुणनफल है और (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5)। संयुग्मी गुणनफल में बीच का अपरिमेय भाग हट जाता है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि \(a+\sqrt{b}\) और \(a-\sqrt{b}\) किसी एकक द्विघात बहुपद के शून्यक हैं, तो स्थिर पद क्या होगा?
If \(a+\sqrt{b}\) and \(a-\sqrt{b}\) are zeroes of a monic quadratic polynomial, what is the constant term?
#general-form
#conjugates
#constant-term
A \(a^2-b\)
B \(a^2+b\)
C (2a)
D (-2a)
Explanation opens after your attempt
Correct Answer
A. \(a^2-b\)
Step 1
Concept
In a monic polynomial, the constant term is the product of zeroes. Here the product is (\(a+\sqrt{b}\)\(a-\sqrt{b}\)=a-2 -b).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-b\). In a monic polynomial, the constant term is the product of zeroes. Here the product is (\(a+\sqrt{b}\)\(a-\sqrt{b}\)=a-2 -b).
Step 3
Exam Tip
एकक बहुपद में स्थिर पद शून्यकों का गुणनफल होता है। यहाँ गुणनफल (\(a+\sqrt{b}\)\(a-\sqrt{b}\)=a-2 -b) है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि शून्यकों का योग \(2\sqrt{5}\) और गुणनफल (4) है, तो एक मानक द्विघात बहुपद कौन सा होगा?
If the sum of zeroes is \(2\sqrt{5}\) and the product is (4), which is a monic quadratic polynomial?
#polynomial-formation
#sum-product
#irrational
A \(x^2-2\sqrt{5}x+4\)
B \(x^2+2\sqrt{5}x+4\)
C \(x^2-4x+2\sqrt{5}\)
D \(x^2+4x-2\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-2\sqrt{5}x+4\)
Step 1
Concept
\(A monic polynomial is (x^2-(\)sum)x+product\(). So the answer is (x^2-2\sqrt{5}x+4).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-2\sqrt{5}x+4). A monic polynomial is (x^2-(\)sum)x+product\(). So the answer is (x^2-2\sqrt{5}x+4).\)
Step 3
Exam Tip
\(मानक बहुपद (x^2-(\)योग)x+गुणनफल) होता है। \(इसलिए उत्तर (x^2-2\sqrt{5}x+4) है\)।
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