यदि \(x^2-8x+15=0\) के मूल \(\alpha\) और \(\beta\) हैं तो (\(\alpha-1\)) और (\(\beta-1\)) का गुणनफल क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-8x+15=0\), what is the product of (\(\alpha-1\)) and (\(\beta-1\))?
#roots
#transformed_expression
#product
A (8)
B (15)
C (7)
D (6)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=8\) and \(\alpha\beta=15\). (\(\alpha-1\)\(\beta-1\)=15-8+1=8).
Step 2
Why this answer is correct
The correct answer is A. (8). Here \(\alpha+\beta=8\) and \(\alpha\beta=15\). (\(\alpha-1\)\(\beta-1\)=15-8+1=8).
Step 3
Exam Tip
यहां \(\alpha+\beta=8\) और \(\alpha\beta=15\) है। (\(\alpha-1\)\(\beta-1\)=15-8+1=8) है।
Login to save your score, XP, coins and progress. Login
यदि मूलों का योग (4) और उनके वर्गों का योग (20) है तो मूलों का गुणनफल क्या होगा?
If the sum of roots is (4) and the sum of their squares is (20), what is the product of roots?
#roots
#identity
#product
A (-2)
B (2)
C (8)
D (-8)
Explanation opens after your attempt
Step 1
Concept
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). From \(20=16-2\alpha\beta\), we get \(\alpha\beta=-2\).
Step 2
Why this answer is correct
The correct answer is A. (-2). (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). From \(20=16-2\alpha\beta\), we get \(\alpha\beta=-2\).
Step 3
Exam Tip
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta) है। \(20=16-2\alpha\beta\) से \(\alpha\beta=-2\) मिलता है।
Login to save your score, XP, coins and progress. Login
समीकरण \(x^2-4x-12=0\) के मूलों को (1) घटाने पर नए मूलों का गुणनफल क्या होगा?
If each root of \(x^2-4x-12=0\) is decreased by (1), what is the product of the new roots?
#roots
#transformed_roots
#product
A (-15)
B (-12)
C (15)
D (12)
Explanation opens after your attempt
Step 1
Concept
The old roots are (6) and (-2). The new roots are (5) and (-3), so the product is (-15).
Step 2
Why this answer is correct
The correct answer is A. (-15). The old roots are (6) and (-2). The new roots are (5) and (-3), so the product is (-15).
Step 3
Exam Tip
पुराने मूल (6) और (-2) हैं। नए मूल (5) और (-3) होंगे इसलिए गुणनफल (-15) है।
Login to save your score, XP, coins and progress. Login
यदि किसी द्विघात समीकरण के मूल (c) और (-c) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{d}{a}\) का मान क्या होगा?
If the roots of a quadratic equation are (c) and (-c), what is the value of the ratio \(\frac{d}{a}\) of constant term to leading coefficient?
#roots
#opposite_roots
#product
A \(-c^2\)
B \(c^2\)
C (0)
D (2c)
Explanation opens after your attempt
Correct Answer
A. \(-c^2\)
Step 1
Concept
\(\frac{d}{a}\) is the product of roots. Here (c(-c)=-c-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(-c^2\). \(\frac{d}{a}\) is the product of roots. Here (c(-c)=-c-2 ).
Step 3
Exam Tip
\(\frac{d}{a}\) मूलों का गुणनफल होता है। यहां (c(-c)=-c-2 ) है।
Login to save your score, XP, coins and progress. Login
समीकरण \(x^2-17x+70=0\) का एक मूल (7) है तो दूसरा मूल क्या है?
If one root of \(x^2-17x+70=0\) is (7), what is the other root?
#roots
#other_root
#product
A (10)
B (7)
C (17)
D (70)
Explanation opens after your attempt
Step 1
Concept
The product of roots is (70) and one root is (7). The other root is \(\frac{70}{7}=10\).
Step 2
Why this answer is correct
The correct answer is A. (10). The product of roots is (70) and one root is (7). The other root is \(\frac{70}{7}=10\).
Step 3
Exam Tip
मूलों का गुणनफल (70) है और एक मूल (7) है। दूसरा मूल \(\frac{70}{7}=10\) होगा।
Login to save your score, XP, coins and progress. Login
यदि किसी द्विघात समीकरण के मूल (b) और (-b) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{c}{a}\) का मान क्या होगा?
If the roots of a quadratic equation are (b) and (-b), what is the value of the ratio \(\frac{c}{a}\) of constant term to leading coefficient?
#roots
#opposite_roots
#product
A \(-b^2\)
B \(b^2\)
C (0)
D (2b)
Explanation opens after your attempt
Correct Answer
A. \(-b^2\)
Step 1
Concept
\(\frac{c}{a}\) is the product of roots. Here (b(-b)=-b-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(-b^2\). \(\frac{c}{a}\) is the product of roots. Here (b(-b)=-b-2 ).
Step 3
Exam Tip
\(\frac{c}{a}\) मूलों का गुणनफल होता है। यहां (b(-b)=-b-2 ) है।
Login to save your score, XP, coins and progress. Login
समीकरण \(x^2-15x+54=0\) का एक मूल (6) है तो दूसरा मूल क्या है?
If one root of \(x^2-15x+54=0\) is (6), what is the other root?
#roots
#other_root
#product
A (9)
B (6)
C (15)
D (54)
Explanation opens after your attempt
Step 1
Concept
The product of roots is (54) and one root is (6). Therefore the other root is \(\frac{54}{6}=9\).
Step 2
Why this answer is correct
The correct answer is A. (9). The product of roots is (54) and one root is (6). Therefore the other root is \(\frac{54}{6}=9\).
Step 3
Exam Tip
मूलों का गुणनफल (54) है और एक मूल (6) है। इसलिए दूसरा मूल \(\frac{54}{6}=9\) है।
Login to save your score, XP, coins and progress. Login
यदि किसी द्विघात समीकरण के मूल (a) और (-a) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{c}{a_1}\) का मान क्या होगा?
If the roots of a quadratic equation are (a) and (-a), what is the value of the ratio \(\frac{c}{a_1}\) of constant term to leading coefficient?
#roots
#opposite_roots
#product
A \(-a^2\)
B \(a^2\)
C (0)
D (2a)
Explanation opens after your attempt
Correct Answer
A. \(-a^2\)
Step 1
Concept
\(\frac{c}{a_1}\) is the product of roots. Here (a(-a)=-a-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(-a^2\). \(\frac{c}{a_1}\) is the product of roots. Here (a(-a)=-a-2 ).
Step 3
Exam Tip
\(\frac{c}{a_1}\) मूलों का गुणनफल होता है। यहां (a(-a)=-a-2 ) है।
Login to save your score, XP, coins and progress. Login
समीकरण \(x^2-13x+40=0\) का एक मूल (5) है तो दूसरा मूल क्या है?
If one root of \(x^2-13x+40=0\) is (5), what is the other root?
#roots
#other_root
#product
A (8)
B (5)
C (13)
D (40)
Explanation opens after your attempt
Step 1
Concept
The product of roots is (40) and one root is (5). Therefore the other root is \(\frac{40}{5}=8\).
Step 2
Why this answer is correct
The correct answer is A. (8). The product of roots is (40) and one root is (5). Therefore the other root is \(\frac{40}{5}=8\).
Step 3
Exam Tip
मूलों का गुणनफल (40) है और एक मूल (5) है। इसलिए दूसरा मूल \(\frac{40}{5}=8\) है।
Login to save your score, XP, coins and progress. Login
यदि किसी द्विघात समीकरण के मूल (r) और (r) हैं तो उनके गुणनफल का मान क्या होगा?
If the roots of a quadratic equation are (r) and (r), what will be their product?
#roots
#equal_roots
#product
A (2r)
B (0)
C \(r^2\)
D (r)
Explanation opens after your attempt
Correct Answer
C. \(r^2\)
Step 1
Concept
The product of (r) and (r) is \(r^2\). For equal roots, remember sum (2r) and product \(r^2\).
Step 2
Why this answer is correct
The correct answer is C. \(r^2\). The product of (r) and (r) is \(r^2\). For equal roots, remember sum (2r) and product \(r^2\).
Step 3
Exam Tip
(r) और (r) का गुणनफल \(r^2\) होता है। बराबर मूलों में योग (2r) और गुणनफल \(r^2\) याद रखें।
Login to save your score, XP, coins and progress. Login
यदि एक मूल (6) है और मूलों का गुणनफल (48) है तो दूसरा मूल क्या होगा?
If one root is (6) and the product of roots is (48), what is the other root?
#roots
#other_root
#product
A (6)
B (8)
C (42)
D (48)
Explanation opens after your attempt
Step 1
Concept
The other root is \(\frac{48}{6}=8\). Divide the product by the given root.
Step 2
Why this answer is correct
The correct answer is B. (8). The other root is \(\frac{48}{6}=8\). Divide the product by the given root.
Step 3
Exam Tip
दूसरा मूल \(\frac{48}{6}=8\) होगा। गुणनफल को दिए हुए मूल से भाग करें।
Login to save your score, XP, coins and progress. Login
यदि एक मूल (5) है और मूलों का गुणनफल (35) है तो दूसरा मूल क्या होगा?
If one root is (5) and the product of roots is (35), what is the other root?
#roots
#other_root
#product
A (5)
B (7)
C (30)
D (35)
Explanation opens after your attempt
Step 1
Concept
The other root is \(\frac{35}{5}=7\). Divide the product by the given root.
Step 2
Why this answer is correct
The correct answer is B. (7). The other root is \(\frac{35}{5}=7\). Divide the product by the given root.
Step 3
Exam Tip
दूसरा मूल \(\frac{35}{5}=7\) होगा। गुणनफल में दिए हुए मूल से भाग करें।
Login to save your score, XP, coins and progress. Login
यदि किसी द्विघात समीकरण के मूल एक दूसरे के व्युत्क्रम हैं तो उनके गुणनफल का मान क्या होगा?
If the roots of a quadratic equation are reciprocals of each other then what is their product?
#roots
#reciprocal_roots
#product
A (0)
B (1)
C (-1)
D (2)
Explanation opens after your attempt
Step 1
Concept
If the roots are (r) and \(\frac{1}{r}\) their product is (1). For reciprocal roots remember the product is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). If the roots are (r) and \(\frac{1}{r}\) their product is (1). For reciprocal roots remember the product is (1).
Step 3
Exam Tip
यदि मूल (r) और \(\frac{1}{r}\) हों तो गुणनफल (1) होता है। व्युत्क्रम मूलों में गुणनफल तुरंत (1) याद रखें।
Login to save your score, XP, coins and progress. Login
यदि एक मूल (3) है और मूलों का गुणनफल (12) है तो दूसरा मूल क्या होगा?
If one root is (3) and the product of roots is (12) then what is the other root?
#roots
#other_root
#product
A (3)
B (4)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
The other root is \(\frac{12}{3}=4\). In product questions divide by the given root.
Step 2
Why this answer is correct
The correct answer is B. (4). The other root is \(\frac{12}{3}=4\). In product questions divide by the given root.
Step 3
Exam Tip
दूसरा मूल \(\frac{12}{3}=4\) होगा। गुणनफल वाले प्रश्न में दिए मूल से भाग दें।
Login to save your score, XP, coins and progress. Login
यदि मूल (-4) और (-9) हैं, तो मूलों का गुणनफल क्या है?
If the roots are (-4) and (-9), what is the product of the roots?
#quadratic-equations
#roots
#product
#medium
A (36)
B (-36)
C (13)
D (-13)
Explanation opens after your attempt
Step 1
Concept
The product of roots is ((-4)(-9)=36). The product of two negative numbers is positive.
Step 2
Why this answer is correct
The correct answer is A. (36). The product of roots is ((-4)(-9)=36). The product of two negative numbers is positive.
Step 3
Exam Tip
मूलों का गुणनफल ((-4)(-9)=36) है। दो ऋणात्मक संख्याओं का गुणनफल धनात्मक होता है।
Login to save your score, XP, coins and progress. Login
यदि मूल (-3) और (-8) हैं, तो मूलों का गुणनफल क्या है?
If the roots are (-3) and (-8), what is the product of the roots?
#quadratic-equations
#roots
#product
#medium
A (24)
B (-24)
C (11)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The product of roots is ((-3)(-8)=24). The product of two negative numbers is positive.
Step 2
Why this answer is correct
The correct answer is A. (24). The product of roots is ((-3)(-8)=24). The product of two negative numbers is positive.
Step 3
Exam Tip
मूलों का गुणनफल ((-3)(-8)=24) है। दो ऋणात्मक संख्याओं का गुणनफल धनात्मक होता है।
Login to save your score, XP, coins and progress. Login
यदि मूल (4) और (6) हैं, तो मूलों का गुणनफल क्या है?
If the roots are (4) and (6), what is the product of the roots?
#quadratic-equations
#roots
#product
#medium
A (10)
B (24)
C (2)
D (-24)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(4\cdot6=24\). Sum and product are both useful while forming an equation from roots.
Step 2
Why this answer is correct
The correct answer is B. (24). The product of roots is \(4\cdot6=24\). Sum and product are both useful while forming an equation from roots.
Step 3
Exam Tip
मूलों का गुणनफल \(4\cdot6=24\) है। मूलों से समीकरण बनाते समय योग और गुणनफल दोनों उपयोगी होते हैं।
Login to save your score, XP, coins and progress. Login
यदि \(\alpha=5+2\sqrt{6}\) और \(\beta=5-2\sqrt{6}\), तो \(\alpha\beta\) क्या है?
If \(\alpha=5+2\sqrt{6}\) and \(\beta=5-2\sqrt{6}\), what is \(\alpha\beta\)?
#conjugates
#product
#irrational-numbers
A (1)
B (25)
C (24)
D (10)
Explanation opens after your attempt
Step 1
Concept
(\alpha\beta=25-\(2\sqrt{6}\)2 =25-24=1). In exams square terms correctly in conjugate multiplication.
Step 2
Why this answer is correct
The correct answer is A. (1). (\alpha\beta=25-\(2\sqrt{6}\)2 =25-24=1). In exams square terms correctly in conjugate multiplication.
Step 3
Exam Tip
(\alpha\beta=25-\(2\sqrt{6}\)2 =25-24=1) है। परीक्षा में संयुग्मी गुणन में वर्ग सही करें।
Login to save your score, XP, coins and progress. Login
यदि \(\alpha=\sqrt{5}+2\) और \(\beta=\sqrt{5}-2\), तो \(\alpha\beta\) क्या है?
If \(\alpha=\sqrt{5}+2\) and \(\beta=\sqrt{5}-2\), what is \(\alpha\beta\)?
#conjugates
#product
#real numbers
A (1)
B (9)
C \(\sqrt{5}\)
D \(4\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
(\alpha\beta=\(\sqrt{5}+2\)\(\sqrt{5}-2\)=5-4=1). Conjugate multiplication often gives a rational answer.
Step 2
Why this answer is correct
The correct answer is A. (1). (\alpha\beta=\(\sqrt{5}+2\)\(\sqrt{5}-2\)=5-4=1). Conjugate multiplication often gives a rational answer.
Step 3
Exam Tip
(\alpha\beta=\(\sqrt{5}+2\)\(\sqrt{5}-2\)=5-4=1) है। परीक्षा में संयुग्मी गुणन से परिमेय उत्तर मिलता है।
Login to save your score, XP, coins and progress. Login
किस द्विघात बहुपद के शून्यक \(\sqrt{7}\) और \(-\sqrt{7}\) हैं?
Which quadratic polynomial has zeroes \(\sqrt{7}\) and \(-\sqrt{7}\)?
#zeroes-to-polynomial
#irrational
#product
A \(x^2+7\)
B \(x^2-7\)
C \(x^2-2\sqrt{7}x+7\)
D \(x^2+2\sqrt{7}x-7\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-7\)
Step 1
Concept
\(The sum of zeroes is (0) and product is (-7), so the polynomial is (x^2-7). Use (x^2-\)sumx+product) to form a polynomial from zeroes.
Step 2
Why this answer is correct
\(The correct answer is B. (x^2-7). The sum of zeroes is (0) and product is (-7), so the polynomial is (x^2-7). Use (x^2-\)sumx+product) to form a polynomial from zeroes.
Step 3
Exam Tip
शून्यकों का योग (0) और गुणनफल (-7) है, इसलिए बहुपद \(x^2-7\) है। \(शून्यकों से बहुपद बनाते समय (x^2-\)योगx+गुणनफल) प्रयोग करें।
Login to save your score, XP, coins and progress. Login
यदि शून्यक \(2\sqrt{2}\) और \(3\sqrt{2}\) हैं, तो बहुपद का स्थिर पद क्या होगा यदि अग्र गुणांक (1) है?
If the zeroes are \(2\sqrt{2}\) and \(3\sqrt{2}\), what is the constant term if the leading coefficient is (1)?
#constant-term
#product
#irrational-zeroes
A (12)
B \(5\sqrt{2}\)
C \(6\sqrt{2}\)
D (10)
Explanation opens after your attempt
Step 1
Concept
The constant term equals the product of the zeroes. (\(2\sqrt{2}\)\(3\sqrt{2}\)=12).
Step 2
Why this answer is correct
The correct answer is A. (12). The constant term equals the product of the zeroes. (\(2\sqrt{2}\)\(3\sqrt{2}\)=12).
Step 3
Exam Tip
स्थिर पद शून्यकों के गुणनफल के बराबर है। (\(2\sqrt{2}\)\(3\sqrt{2}\)=12) है।
Login to save your score, XP, coins and progress. Login
यदि \(\alpha=\sqrt{3}+1\) और \(\beta=\sqrt{3}-1\), तो \(\alpha\beta\) क्या है?
If \(\alpha=\sqrt{3}+1\) and \(\beta=\sqrt{3}-1\), what is \(\alpha\beta\)?
#conjugate
#product
#irrational-numbers
A (2)
B (4)
C \(\sqrt{3}\)
D \(3+\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
(\alpha\beta=\(\sqrt{3}+1\)\(\sqrt{3}-1\)=3-1=2). The irrational part cancels in conjugate multiplication.
Step 2
Why this answer is correct
The correct answer is A. (2). (\alpha\beta=\(\sqrt{3}+1\)\(\sqrt{3}-1\)=3-1=2). The irrational part cancels in conjugate multiplication.
Step 3
Exam Tip
(\alpha\beta=\(\sqrt{3}+1\)\(\sqrt{3}-1\)=3-1=2) है। संयुग्मी गुणनफल से अपरिमेय भाग कट जाता है।
Login to save your score, XP, coins and progress. Login
यदि \(a=\sqrt{7}+\sqrt{2}\) और \(b=\sqrt{7}-\sqrt{2}\) हैं तो (ab) का मान क्या है?
If \(a=\sqrt{7}+\sqrt{2}\) and \(b=\sqrt{7}-\sqrt{2}\), what is the value of (ab)?
#conjugate
#product
#rational-result
A (5)
B (9)
C \(\sqrt{14}\)
D \(7+2\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
In conjugate multiplication, (ab=7-2=5). The difference of squares formula gives the answer quickly.
Step 2
Why this answer is correct
The correct answer is A. (5). In conjugate multiplication, (ab=7-2=5). The difference of squares formula gives the answer quickly.
Step 3
Exam Tip
संयुग्मी गुणन में (ab=7-2=5) होता है। अंतर वर्ग सूत्र जल्दी उत्तर देता है।
Login to save your score, XP, coins and progress. Login
यदि \(p=7+\sqrt{11}\) और \(q=7-\sqrt{11}\) हैं तो (pq) का मान क्या है?
If \(p=7+\sqrt{11}\) and \(q=7-\sqrt{11}\), what is the value of (pq)?
#conjugate
#surds
#product
A (38)
B (60)
C \(14\sqrt{11}\)
D \(49+\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
Conjugate multiplication gives (pq=72 -\(\sqrt{11}\)2 =49-11=38). Use \(a^2-b^2\) in such questions.
Step 2
Why this answer is correct
The correct answer is A. (38). Conjugate multiplication gives (pq=72 -\(\sqrt{11}\)2 =49-11=38). Use \(a^2-b^2\) in such questions.
Step 3
Exam Tip
संयुग्मी गुणन से (pq=72 -\(\sqrt{11}\)2 =49-11=38) मिलता है। ऐसे प्रश्नों में \(a^2-b^2\) लगाएँ।
Login to save your score, XP, coins and progress. Login
यदि ग्राफ (x=-12) और (x=12) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?
If a graph cuts the (x)-axis at (x=-12) and (x=12), what are the product and sum of the zeroes?
#opposite zeroes
#product
#sum
A गुणनफल (-144), योग (0) / Product (-144), sum (0)
B गुणनफल (144), योग (0) / Product (144), sum (0)
C गुणनफल (0), योग (24) / Product (0), sum (24)
D गुणनफल (-24), योग (144) / Product (-24), sum (144)
Explanation opens after your attempt
Correct Answer
A. गुणनफल (-144), योग (0) / Product (-144), sum (0)
Step 1
Concept
The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 2
Why this answer is correct
The correct answer is A. गुणनफल (-144), योग (0) / Product (-144), sum (0). The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 3
Exam Tip
शून्यक (-12) और (12) हैं, इसलिए गुणनफल (-144) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।
Login to save your score, XP, coins and progress. Login
यदि ग्राफ (x=-10) और (x=10) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?
If a graph cuts the (x)-axis at (x=-10) and (x=10), what are the product and sum of the zeroes?
#opposite zeroes
#product
#sum
A गुणनफल (-100), योग (0) / Product (-100), sum (0)
B गुणनफल (100), योग (0) / Product (100), sum (0)
C गुणनफल (0), योग (20) / Product (0), sum (20)
D गुणनफल (-20), योग (100) / Product (-20), sum (100)
Explanation opens after your attempt
Correct Answer
A. गुणनफल (-100), योग (0) / Product (-100), sum (0)
Step 1
Concept
The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 2
Why this answer is correct
The correct answer is A. गुणनफल (-100), योग (0) / Product (-100), sum (0). The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 3
Exam Tip
शून्यक (-10) और (10) हैं, इसलिए गुणनफल (-100) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।
Login to save your score, XP, coins and progress. Login
यदि ग्राफ के (x)-अक्ष कटान ((a,0)), ((b,0)), ((c,0)) हैं, तो शून्यकों का गुणनफल क्या होगा?
If the (x)-axis intersections of a graph are ((a,0)), ((b,0)), ((c,0)), what will be the product of the zeroes?
#symbolic zeroes
#product
#coordinates
A (a+b+c)
B (abc)
C (0)
D (ab+c)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (a), (b), (c), so their product is (abc). Tip: even in symbolic points, the first coordinate is the zero.
Step 2
Why this answer is correct
The correct answer is B. (abc). The zeroes are (a), (b), (c), so their product is (abc). Tip: even in symbolic points, the first coordinate is the zero.
Step 3
Exam Tip
शून्यक (a), (b), (c) हैं, इसलिए गुणनफल (abc) है। टिप: प्रतीकात्मक बिंदु में भी पहला निर्देशांक शून्यक है।
Login to save your score, XP, coins and progress. Login
यदि किसी ग्राफ के (x)-अक्ष कटान ((m,0)) और ((n,0)) हैं, तो शून्यकों का गुणनफल क्या होगा?
If the (x)-axis intersections of a graph are ((m,0)) and ((n,0)), what is the product of the zeroes?
#general rule
#product
#zeroes
A (m+n)
B (mn)
C (0)
D (m-n)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (m) and (n), so the product is (mn). Tip: the first coordinate of the intersection point is the zero.
Step 2
Why this answer is correct
The correct answer is B. (mn). The zeroes are (m) and (n), so the product is (mn). Tip: the first coordinate of the intersection point is the zero.
Step 3
Exam Tip
शून्यक (m) और (n) हैं, इसलिए गुणनफल (mn) है। टिप: कटान बिंदु का पहला निर्देशांक ही शून्यक है।
Login to save your score, XP, coins and progress. Login
कौन सा गुणनफल अपरिमेय है?
Which product is irrational?
#product
#irrational numbers
#class 10
A \(0\cdot \sqrt{11}\)
B \(\sqrt{8}\cdot \sqrt{2}\)
C \(\frac{3}{5}\cdot \sqrt{13}\)
D \(\sqrt{3}\cdot \sqrt{12}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{3}{5}\cdot \sqrt{13}\)
Step 1
Concept
\(\frac{3}{5}\) is a non-zero rational number.
Step 2
Why this answer is correct
Multiplying it by \(\sqrt{13}\) gives an irrational number.
Step 3
Exam Tip
In products check first whether square roots combine to a perfect square. चरण 1: \(\frac{3}{5}\) शून्य रहित परिमेय है। चरण 2: शून्य रहित परिमेय संख्या से \(\sqrt{13}\) को गुणा करने पर अपरिमेय संख्या मिलती है। चरण 3: गुणनफल में पहले देखें कि वर्गमूल मिलकर पूर्ण वर्ग तो नहीं बना रहे।
Login to save your score, XP, coins and progress. Login
\(\sqrt{7}\) और \(-\sqrt{7}\) का गुणनफल क्या होगा?
What is the product of \(\sqrt{7}\) and \(-\sqrt{7}\)?
#real-numbers
#square-root
#product
A (7)
B (-7)
C \(\sqrt{14}\)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{7}\times\sqrt{7}=7\).
Step 2
Why this answer is correct
Because there is one negative sign, the product is (-7).
Step 3
Exam Tip
Pay attention to both the sign and the square root. चरण 1: \(\sqrt{7}\times\sqrt{7}=7\) होता है। चरण 2: एक ऋण चिह्न होने से गुणनफल (-7) होगा। चरण 3: चिह्न और वर्गमूल दोनों पर ध्यान दें।
Login to save your score, XP, coins and progress. Login
