यदि \(\alpha\) और \(\beta\) समीकरण \(x^2-9x+20=0\) के मूल हैं तो \(\alpha+\beta+\alpha\beta\) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-9x+20=0\), what is the value of \(\alpha+\beta+\alpha\beta\)?
#roots
#sum_product
#expression
A (29)
B (20)
C (9)
D (11)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=9\) and \(\alpha\beta=20\). Therefore the total is (9+20=29).
Step 2
Why this answer is correct
The correct answer is A. (29). Here \(\alpha+\beta=9\) and \(\alpha\beta=20\). Therefore the total is (9+20=29).
Step 3
Exam Tip
यहां \(\alpha+\beta=9\) और \(\alpha\beta=20\) है। इसलिए कुल (9+20=29) है।
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समीकरण \(5x^2-18x+9=0\) के मूलों का योग और गुणनफल क्रमशः क्या हैं?
For \(5x^2-18x+9=0\), what are the sum and product of roots respectively?
#roots
#sum_product
#formula
A \(\frac{18}{5}\) और \(\frac{9}{5}\) / \(\frac{18}{5}\) and \(\frac{9}{5}\)
B -\(\frac{18}{5}\) और \(\frac{9}{5}\) / \(-\frac{18}{5}\) and \(\frac{9}{5}\)
C \(\frac{18}{5}\) और \(-\frac{9}{5}\) / \(\frac{18}{5}\) and \(-\frac{9}{5}\)
D (18) और (9) / (18) and (9)
Explanation opens after your attempt
Correct Answer
A. \(\frac{18}{5}\) और \(\frac{9}{5}\) / \(\frac{18}{5}\) and \(\frac{9}{5}\)
Step 1
Concept
The sum is \(-\frac{b}{a}=\frac{18}{5}\) and the product is \(\frac{c}{a}=\frac{9}{5}\). Identify (a), (b), and (c) first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{18}{5}\) और \(\frac{9}{5}\) / \(\frac{18}{5}\) and \(\frac{9}{5}\). The sum is \(-\frac{b}{a}=\frac{18}{5}\) and the product is \(\frac{c}{a}=\frac{9}{5}\). Identify (a), (b), and (c) first.
Step 3
Exam Tip
योग \(-\frac{b}{a}=\frac{18}{5}\) और गुणनफल \(\frac{c}{a}=\frac{9}{5}\) है। पहले (a), (b), (c) पहचानें।
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यदि मूल \(\alpha\) और \(\beta\) हैं तथा \(\alpha+\beta=8\) और \(\alpha\beta=15\) है तो \(\alpha^2+\beta^2\) का मान क्या है?
If the roots are \(\alpha\) and \(\beta\) with \(\alpha+\beta=8\) and \(\alpha\beta=15\), what is \(\alpha^2+\beta^2\)?
#roots
#identity
#sum_product
A (34)
B (49)
C (64)
D (30)
Explanation opens after your attempt
Step 1
Concept
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=64-30=34). Use identities in such questions.
Step 2
Why this answer is correct
The correct answer is A. (34). (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=64-30=34). Use identities in such questions.
Step 3
Exam Tip
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=64-30=34) है। ऐसे प्रश्नों में पहचान का प्रयोग करें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(2x^2-7x+3=0\) के मूल हैं तो \(\alpha+\beta-\alpha\beta\) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(2x^2-7x+3=0\), what is the value of \(\alpha+\beta-\alpha\beta\)?
#roots
#sum_product
#expression
A (2)
B \(\frac{7}{2}\)
C \(\frac{3}{2}\)
D (5)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\). Therefore \(\alpha+\beta-\alpha\beta=\frac{7}{2}-\frac{3}{2}=2\).
Step 2
Why this answer is correct
The correct answer is A. (2). Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\). Therefore \(\alpha+\beta-\alpha\beta=\frac{7}{2}-\frac{3}{2}=2\).
Step 3
Exam Tip
यहां \(\alpha+\beta=\frac{7}{2}\) और \(\alpha\beta=\frac{3}{2}\) है। इसलिए \(\alpha+\beta-\alpha\beta=\frac{7}{2}-\frac{3}{2}=2\) होगा।
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समीकरण \(x^2-18x+81=0\) के मूलों का योग और गुणनफल क्रमशः क्या हैं?
For \(x^2-18x+81=0\), what are the sum and product of roots respectively?
#roots
#repeated_root
#sum_product
A (18) और (81) / (18) and (81)
B -(18) और (81) / (-18) and (81)
C (9) और (9) / (9) and (9)
D (81) और (18) / (81) and (18)
Explanation opens after your attempt
Correct Answer
A. (18) और (81) / (18) and (81)
Step 1
Concept
It is ((x-9)2 =0), so both roots are (9). The sum is (18) and the product is (81).
Step 2
Why this answer is correct
The correct answer is A. (18) और (81) / (18) and (81). It is ((x-9)2 =0), so both roots are (9). The sum is (18) and the product is (81).
Step 3
Exam Tip
यह ((x-9)2 =0) है इसलिए दोनों मूल (9) हैं। योग (18) और गुणनफल (81) होगा।
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यदि \(\alpha+\beta=-5\) और \(\alpha\beta=-14\) है तो \(\alpha\) और \(\beta\) के लिए मोनिक समीकरण कौन सा है?
If \(\alpha+\beta=-5\) and \(\alpha\beta=-14\), which monic equation has roots \(\alpha\) and \(\beta\)?
#roots
#equation_from_roots
#sum_product
A \(x^2+5x-14=0\)
B \(x^2-5x-14=0\)
C \(x^2+14x-5=0\)
D \(x^2-14x+5=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x-14=0\)
Step 1
Concept
The monic equation is (x-2 -\(\alpha+\beta\)x+\alpha\beta=0). Therefore \(x^2+5x-14=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x-14=0\). The monic equation is (x-2 -\(\alpha+\beta\)x+\alpha\beta=0). Therefore \(x^2+5x-14=0\) is correct.
Step 3
Exam Tip
मोनिक समीकरण (x-2 -\(\alpha+\beta\)x+\alpha\beta=0) होता है। इसलिए \(x^2+5x-14=0\) सही है।
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यदि \(\alpha\) और \(\beta\) समीकरण \(x^2-8x+15=0\) के मूल हैं तो \(\alpha+\beta+\alpha\beta\) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-8x+15=0\), what is the value of \(\alpha+\beta+\alpha\beta\)?
#roots
#sum_product
#expression
A (23)
B (15)
C (8)
D (7)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=8\) and \(\alpha\beta=15\). Therefore the total is (8+15=23).
Step 2
Why this answer is correct
The correct answer is A. (23). Here \(\alpha+\beta=8\) and \(\alpha\beta=15\). Therefore the total is (8+15=23).
Step 3
Exam Tip
यहां \(\alpha+\beta=8\) और \(\alpha\beta=15\) है। इसलिए कुल (8+15=23) है।
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समीकरण \(3x^2-14x+8=0\) के मूलों का योग और गुणनफल क्रमशः क्या हैं?
For \(3x^2-14x+8=0\), what are the sum and product of roots respectively?
#roots
#sum_product
#formula
A \(\frac{14}{3}\) और \(\frac{8}{3}\) / \(\frac{14}{3}\) and \(\frac{8}{3}\)
B -\(\frac{14}{3}\) और \(\frac{8}{3}\) / \(-\frac{14}{3}\) and \(\frac{8}{3}\)
C \(\frac{14}{3}\) और \(-\frac{8}{3}\) / \(\frac{14}{3}\) and \(-\frac{8}{3}\)
D (14) और (8) / (14) and (8)
Explanation opens after your attempt
Correct Answer
A. \(\frac{14}{3}\) और \(\frac{8}{3}\) / \(\frac{14}{3}\) and \(\frac{8}{3}\)
Step 1
Concept
The sum is \(-\frac{b}{a}=\frac{14}{3}\) and the product is \(\frac{c}{a}=\frac{8}{3}\). Identify (a), (b), and (c) first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{14}{3}\) और \(\frac{8}{3}\) / \(\frac{14}{3}\) and \(\frac{8}{3}\). The sum is \(-\frac{b}{a}=\frac{14}{3}\) and the product is \(\frac{c}{a}=\frac{8}{3}\). Identify (a), (b), and (c) first.
Step 3
Exam Tip
योग \(-\frac{b}{a}=\frac{14}{3}\) और गुणनफल \(\frac{c}{a}=\frac{8}{3}\) है। पहले (a), (b), (c) पहचानें।
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यदि मूल \(\alpha\) और \(\beta\) हैं तथा \(\alpha+\beta=7\) और \(\alpha\beta=12\) है तो \(\alpha^2+\beta^2\) का मान क्या है?
If the roots are \(\alpha\) and \(\beta\) with \(\alpha+\beta=7\) and \(\alpha\beta=12\), what is \(\alpha^2+\beta^2\)?
#roots
#identity
#sum_product
A (25)
B (37)
C (49)
D (84)
Explanation opens after your attempt
Step 1
Concept
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=49-24=25). Use identities in such questions.
Step 2
Why this answer is correct
The correct answer is A. (25). (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=49-24=25). Use identities in such questions.
Step 3
Exam Tip
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=49-24=25) है। ऐसे प्रश्नों में पहचान का प्रयोग करें।
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यदि \(\alpha\) और \(\beta\) समीकरण \(3x^2-4x-4=0\) के मूल हैं तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(3x^2-4x-4=0\), what is the value of \(\frac{1}{\alpha}+\frac{1}{\beta}\)?
#roots
#reciprocal_sum
#sum_product
A (-1)
B (1)
C \(-\frac{4}{3}\)
D \(\frac{4}{3}\)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=\frac{4}{3}\) and \(\alpha\beta=-\frac{4}{3}\). Therefore \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=-1\).
Step 2
Why this answer is correct
The correct answer is A. (-1). Here \(\alpha+\beta=\frac{4}{3}\) and \(\alpha\beta=-\frac{4}{3}\). Therefore \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=-1\).
Step 3
Exam Tip
यहां \(\alpha+\beta=\frac{4}{3}\) और \(\alpha\beta=-\frac{4}{3}\) है। इसलिए \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=-1\) होगा।
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समीकरण \(x^2-14x+49=0\) के मूलों का योग और गुणनफल क्रमशः क्या हैं?
For \(x^2-14x+49=0\), what are the sum and product of roots respectively?
#roots
#repeated_root
#sum_product
A (14) और (49) / (14) and (49)
B (-14) और (49) / (-14) and (49)
C (7) और (7) / (7) and (7)
D (49) और (14) / (49) and (14)
Explanation opens after your attempt
Correct Answer
A. (14) और (49) / (14) and (49)
Step 1
Concept
It is ((x-7)2 =0), so both roots are (7). The sum is (14) and the product is (49).
Step 2
Why this answer is correct
The correct answer is A. (14) और (49) / (14) and (49). It is ((x-7)2 =0), so both roots are (7). The sum is (14) and the product is (49).
Step 3
Exam Tip
यह ((x-7)2 =0) है इसलिए दोनों मूल (7) हैं। योग (14) और गुणनफल (49) होगा।
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यदि \(\alpha+\beta=-3\) और \(\alpha\beta=-10\) है तो \(\alpha\) और \(\beta\) के लिए मोनिक समीकरण कौन सा है?
If \(\alpha+\beta=-3\) and \(\alpha\beta=-10\), which monic equation has roots \(\alpha\) and \(\beta\)?
#roots
#equation_from_roots
#sum_product
A \(x^2+3x-10=0\)
B \(x^2-3x-10=0\)
C \(x^2+10x-3=0\)
D \(x^2-10x+3=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-10=0\)
Step 1
Concept
The monic equation is (x-2 -\(\alpha+\beta\)x+\alpha\beta=0). Therefore \(x^2+3x-10=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-10=0\). The monic equation is (x-2 -\(\alpha+\beta\)x+\alpha\beta=0). Therefore \(x^2+3x-10=0\) is correct.
Step 3
Exam Tip
मोनिक समीकरण (x-2 -\(\alpha+\beta\)x+\alpha\beta=0) होता है। इसलिए \(x^2+3x-10=0\) सही है।
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यदि \(\alpha\) और \(\beta\) समीकरण \(x^2-5x+6=0\) के मूल हैं तो \(\alpha+\beta+\alpha\beta\) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-5x+6=0\), what is the value of \(\alpha+\beta+\alpha\beta\)?
#roots
#sum_product
#expression
A (11)
B (5)
C (6)
D (1)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=5\) and \(\alpha\beta=6\). Therefore the total is (5+6=11).
Step 2
Why this answer is correct
The correct answer is A. (11). Here \(\alpha+\beta=5\) and \(\alpha\beta=6\). Therefore the total is (5+6=11).
Step 3
Exam Tip
यहां \(\alpha+\beta=5\) और \(\alpha\beta=6\) है। इसलिए कुल (5+6=11) है।
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समीकरण \(2x^2-9x+4=0\) के मूलों का योग और गुणनफल क्रमशः क्या हैं?
For \(2x^2-9x+4=0\), what are the sum and product of roots respectively?
#roots
#sum_product
#formula
A \(\frac{9}{2}\) और (2) / \(\frac{9}{2}\) and (2)
B -\(\frac{9}{2}\) और (2) / \(-\frac{9}{2}\) and (2)
C \(\frac{9}{2}\) और (-2) / \(\frac{9}{2}\) and (-2)
D (9) और (4) / (9) and (4)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9}{2}\) और (2) / \(\frac{9}{2}\) and (2)
Step 1
Concept
The sum is \(-\frac{b}{a}=\frac{9}{2}\) and the product is \(\frac{c}{a}=2\). Identify (a), (b), and (c) first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{2}\) और (2) / \(\frac{9}{2}\) and (2). The sum is \(-\frac{b}{a}=\frac{9}{2}\) and the product is \(\frac{c}{a}=2\). Identify (a), (b), and (c) first.
Step 3
Exam Tip
योग \(-\frac{b}{a}=\frac{9}{2}\) और गुणनफल \(\frac{c}{a}=2\) है। पहले (a), (b), (c) पहचानें।
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यदि मूल \(\alpha\) और \(\beta\) हैं तथा \(\alpha+\beta=6\) और \(\alpha\beta=8\) है तो \(\alpha^2+\beta^2\) का मान क्या है?
If the roots are \(\alpha\) and \(\beta\) with \(\alpha+\beta=6\) and \(\alpha\beta=8\), what is \(\alpha^2+\beta^2\)?
#roots
#identity
#sum_product
A (20)
B (28)
C (36)
D (48)
Explanation opens after your attempt
Step 1
Concept
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=36-16=20). Use identities in such questions.
Step 2
Why this answer is correct
The correct answer is A. (20). (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=36-16=20). Use identities in such questions.
Step 3
Exam Tip
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=36-16=20) है। ऐसे प्रश्नों में पहचान का प्रयोग करें।
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किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-169) है?
Which quadratic equation has sum of roots (0) and product (-169)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-169=0\)
B \(x^2+169=0\)
C \(x^2+13x-169=0\)
D \(x^2-13x-169=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-169=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-169=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-169) रखने पर (x^2-169=0) मिलता है\)।
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दो संख्याओं का योग (19) और गुणनफल (90) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (19) and product (90). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-19x+90=0\)
B \(x^2+19x+90=0\)
C \(x^2-90x+19=0\)
D \(x^2+90x-19=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-19x+90=0\)
Step 1
Concept
If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-19x+90=0\). If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (19) और गुणनफल (90) है, तो समीकरण \(x^2-19x+90=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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किस विकल्प में मूलों का योग धनात्मक और गुणनफल धनात्मक होगा?
In which option will the sum of roots be positive and the product of roots be positive?
#quadratic-equations
#sum-product
#signs
#expert
A \(x^2-9x+20=0\)
B \(x^2+9x+20=0\)
C \(x^2-9x-20=0\)
D \(x^2+9x-20=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-9x+20=0\)
Step 1
Concept
In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-9x+20=0\). In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.
Step 3
Exam Tip
पहले विकल्प में योग \(-\frac{b}{a}=9\) और गुणनफल \(\frac{c}{a}=20\) है। इसलिए दोनों धनात्मक हैं।
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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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किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-144) है?
Which quadratic equation has sum of roots (0) and product (-144)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-144=0\)
B \(x^2+144=0\)
C \(x^2+12x-144=0\)
D \(x^2-12x-144=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-144=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-144=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-144) रखने पर (x^2-144=0) मिलता है\)।
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दो संख्याओं का योग (17) और गुणनफल (72) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (17) and product (72). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-17x+72=0\)
B \(x^2+17x+72=0\)
C \(x^2-72x+17=0\)
D \(x^2+72x-17=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-17x+72=0\)
Step 1
Concept
If the sum of roots is (17) and product is (72), the equation is \(x^2-17x+72=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-17x+72=0\). If the sum of roots is (17) and product is (72), the equation is \(x^2-17x+72=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (17) और गुणनफल (72) है, तो समीकरण \(x^2-17x+72=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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किस विकल्प में मूलों का योग ऋणात्मक और गुणनफल ऋणात्मक होगा?
In which option will the sum of roots be negative and the product of roots be negative?
#quadratic-equations
#sum-product
#signs
#expert
A \(x^2+5x-24=0\)
B \(x^2-5x-24=0\)
C \(x^2+5x+24=0\)
D \(x^2-5x+24=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x-24=0\)
Step 1
Concept
In the first option, the sum is \(-\frac{b}{a}=-5\) and the product is \(\frac{c}{a}=-24\). So both are negative.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x-24=0\). In the first option, the sum is \(-\frac{b}{a}=-5\) and the product is \(\frac{c}{a}=-24\). So both are negative.
Step 3
Exam Tip
पहले विकल्प में योग \(-\frac{b}{a}=-5\) और गुणनफल \(\frac{c}{a}=-24\) है। इसलिए दोनों ऋणात्मक हैं।
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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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किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-121) है?
Which quadratic equation has sum of roots (0) and product (-121)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-121=0\)
B \(x^2+121=0\)
C \(x^2+11x-121=0\)
D \(x^2-11x-121=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-121=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-121) gives (x^2-121=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-121=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-121) gives (x^2-121=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-121) रखने पर (x^2-121=0) मिलता है\)।
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दो संख्याओं का योग (15) और गुणनफल (54) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (15) and product (54). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-15x+54=0\)
B \(x^2+15x+54=0\)
C \(x^2-54x+15=0\)
D \(x^2+54x-15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-15x+54=0\)
Step 1
Concept
If the sum of roots is (15) and product is (54), the equation is \(x^2-15x+54=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-15x+54=0\). If the sum of roots is (15) and product is (54), the equation is \(x^2-15x+54=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (15) और गुणनफल (54) है, तो समीकरण \(x^2-15x+54=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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किस विकल्प में मूलों का योग धनात्मक और गुणनफल ऋणात्मक होगा?
In which option will the sum of roots be positive and the product of roots be negative?
#quadratic-equations
#sum-product
#signs
#expert
A \(x^2-6x-16=0\)
B \(x^2+6x-16=0\)
C \(x^2-6x+16=0\)
D \(x^2+6x+16=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-6x-16=0\)
Step 1
Concept
In the first option, the sum is \(-\frac{b}{a}=6\) and the product is \(\frac{c}{a}=-16\). So the sum is positive and the product is negative.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-6x-16=0\). In the first option, the sum is \(-\frac{b}{a}=6\) and the product is \(\frac{c}{a}=-16\). So the sum is positive and the product is negative.
Step 3
Exam Tip
पहले विकल्प में योग \(-\frac{b}{a}=6\) और गुणनफल \(\frac{c}{a}=-16\) है। इसलिए योग धनात्मक और गुणनफल ऋणात्मक है।
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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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किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-81) है?
Which quadratic equation has sum of roots (0) and product (-81)?
#quadratic-equations
#sum-product
#forming-equation
#hard
A \(x^2-81=0\)
B \(x^2+81=0\)
C \(x^2+9x-81=0\)
D \(x^2-9x-81=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-81=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-81) gives (x^2-81=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-81=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-81) gives (x^2-81=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-81) रखने पर (x^2-81=0) मिलता है\)।
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दो संख्याओं का योग (13) और गुणनफल (40) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (13) and product (40). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#hard
A \(x^2-13x+40=0\)
B \(x^2+13x+40=0\)
C \(x^2-40x+13=0\)
D \(x^2+40x-13=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-13x+40=0\)
Step 1
Concept
If the sum of roots is (13) and product is (40), the equation is \(x^2-13x+40=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-13x+40=0\). If the sum of roots is (13) and product is (40), the equation is \(x^2-13x+40=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (13) और गुणनफल (40) है, तो समीकरण \(x^2-13x+40=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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किस विकल्प में मूलों का योग ऋणात्मक और गुणनफल धनात्मक होगा?
In which option will the sum of roots be negative and the product of roots be positive?
#quadratic-equations
#sum-product
#signs
#hard
A \(x^2+7x+12=0\)
B \(x^2-7x+12=0\)
C \(x^2+7x-12=0\)
D \(x^2-7x-12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+7x+12=0\)
Step 1
Concept
In the first option, the sum is \(-\frac{b}{a}=-7\) and the product is \(\frac{c}{a}=12\). So the sum is negative and the product is positive.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+7x+12=0\). In the first option, the sum is \(-\frac{b}{a}=-7\) and the product is \(\frac{c}{a}=12\). So the sum is negative and the product is positive.
Step 3
Exam Tip
पहले विकल्प में योग \(-\frac{b}{a}=-7\) और गुणनफल \(\frac{c}{a}=12\) है। इसलिए योग ऋणात्मक और गुणनफल धनात्मक है।
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