समीकरण \(7x^2+5x-14=0\) के मूलों का गुणनफल क्या है?
What is the product of roots of \(7x^2+5x-14=0\)?
#roots
#product_of_roots
#numerical
A (2)
B (-2)
C \(\frac{5}{7}\)
D \(-\frac{5}{7}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{c}{a}\). Here \(\frac{-14}{7}=-2\).
Step 2
Why this answer is correct
The correct answer is B. (-2). The product of roots is \(\frac{c}{a}\). Here \(\frac{-14}{7}=-2\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-14}{7}=-2\) है।
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समीकरण \(6x^2-x-2=0\) के मूलों का गुणनफल क्या है?
What is the product of roots of \(6x^2-x-2=0\)?
#roots
#product_of_roots
#formula
A \(-\frac{1}{3}\)
B \(\frac{1}{3}\)
C \(-\frac{1}{6}\)
D \(\frac{2}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{1}{3}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}\). Here \(\frac{-2}{6}=-\frac{1}{3}\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{1}{3}\). The product of roots is \(\frac{c}{a}\). Here \(\frac{-2}{6}=-\frac{1}{3}\) is correct.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-2}{6}=-\frac{1}{3}\) सही है।
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समीकरण \(5x^2-2x-8=0\) के मूलों का गुणनफल क्या है?
What is the product of roots of \(5x^2-2x-8=0\)?
#roots
#product_of_roots
#numerical
A (8)
B (-8)
C \(-\frac{8}{5}\)
D \(\frac{2}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(-\frac{8}{5}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}\). Here \(\frac{-8}{5}\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(-\frac{8}{5}\). The product of roots is \(\frac{c}{a}\). Here \(\frac{-8}{5}\) is correct.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-8}{5}\) सही है।
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समीकरण \(4x^2+7x-3=0\) के मूलों का गुणनफल क्या है?
What is the product of roots of \(4x^2+7x-3=0\)?
#roots
#product_of_roots
#formula
A \(\frac{3}{4}\)
B \(-\frac{3}{4}\)
C \(\frac{7}{4}\)
D \(-\frac{7}{4}\)
Explanation opens after your attempt
Correct Answer
B. \(-\frac{3}{4}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}\). Here \(\frac{c}{a}=\frac{-3}{4}\).
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{3}{4}\). The product of roots is \(\frac{c}{a}\). Here \(\frac{c}{a}=\frac{-3}{4}\).
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{c}{a}=\frac{-3}{4}\) है।
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समीकरण \(2x^2-3x-2=0\) के मूलों का गुणनफल क्या है?
What is the product of roots of \(2x^2-3x-2=0\)?
#roots
#product_of_roots
#numerical
A (-1)
B (1)
C (-2)
D (2)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{c}{a}\) so \(\frac{-2}{2}=-1\). Identify (a) and (c) first.
Step 2
Why this answer is correct
The correct answer is A. (-1). The product of roots is \(\frac{c}{a}\) so \(\frac{-2}{2}=-1\). Identify (a) and (c) first.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}\) है इसलिए \(\frac{-2}{2}=-1\)। पहले (a) और (c) पहचानें।
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समीकरण \(ax^2+bx+c=0\) के मूल \(\alpha\) और \(\beta\) हों तो \(\alpha\beta\) किसके बराबर होता है?
If \(\alpha\) and \(\beta\) are roots of \(ax^2+bx+c=0\) then what is \(\alpha\beta\)?
#roots
#product_of_roots
#formula
A \(\frac{c}{a}\)
B \(-\frac{b}{a}\)
C \(\frac{b}{c}\)
D \(-\frac{a}{c}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{c}{a}\)
Step 1
Concept
For a quadratic equation the product of roots is \(\frac{c}{a}\). Do not ignore (a).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{c}{a}\). For a quadratic equation the product of roots is \(\frac{c}{a}\). Do not ignore (a).
Step 3
Exam Tip
द्विघात समीकरण में मूलों का गुणनफल \(\frac{c}{a}\) होता है। (a) को नजरअंदाज न करें।
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किस समीकरण के मूलों का गुणनफल ऋणात्मक होगा?
Which equation will have a negative product of roots?
#quadratic-equations
#product-of-roots
#sign
#hard
A \(2x^2+3x-5=0\)
B \(2x^2+3x+5=0\)
C \(2x^2-3x+5=0\)
D \(2x^2-3x+0=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+3x-5=0\)
Step 1
Concept
The product of roots is \(\frac{c}{a}\). In the first option, \(\frac{-5}{2}<0\), so the product is negative.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+3x-5=0\). The product of roots is \(\frac{c}{a}\). In the first option, \(\frac{-5}{2}<0\), so the product is negative.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}\) है। पहले विकल्प में \(\frac{-5}{2}<0\), इसलिए गुणनफल ऋणात्मक है।
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यदि \(qx^2-8x+12=0\) में मूलों का गुणनफल (4) है, तो (q) का मान क्या है?
If the product of roots of \(qx^2-8x+12=0\) is (4), what is the value of (q)?
#quadratic-equations
#parameter
#product-of-roots
#medium
A (3)
B (4)
C (6)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{12}{q}=4\), so (q=3). Use \(\frac{c}{a}\) for the product of roots.
Step 2
Why this answer is correct
The correct answer is A. (3). The product of roots is \(\frac{12}{q}=4\), so (q=3). Use \(\frac{c}{a}\) for the product of roots.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{12}{q}=4\), इसलिए (q=3) है। गुणनफल के लिए \(\frac{c}{a}\) का प्रयोग करें।
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समीकरण \(6x^2+5x-14=0\) में मूलों का गुणनफल क्या है?
What is the product of roots of \(6x^2+5x-14=0\)?
#quadratic-equations
#product-of-roots
#medium
A \(-\frac{7}{3}\)
B \(\frac{7}{3}\)
C \(-\frac{5}{6}\)
D \(\frac{5}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{7}{3}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-14}{6}=-\frac{7}{3}\). Write the answer in simplified form.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{7}{3}\). The product of roots is \(\frac{c}{a}=\frac{-14}{6}=-\frac{7}{3}\). Write the answer in simplified form.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-14}{6}=-\frac{7}{3}\) है। उत्तर को सरल रूप में लिखें।
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यदि \(px^2+6x+9=0\) में मूलों का गुणनफल (3) है, तो (p) का मान क्या है?
If the product of roots of \(px^2+6x+9=0\) is (3), what is the value of (p)?
#quadratic-equations
#parameter
#product-of-roots
#medium
A (3)
B (6)
C (9)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{9}{p}=3\), so (p=3). Use \(\frac{c}{a}\) for the product of roots.
Step 2
Why this answer is correct
The correct answer is A. (3). The product of roots is \(\frac{9}{p}=3\), so (p=3). Use \(\frac{c}{a}\) for the product of roots.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{9}{p}=3\), इसलिए (p=3) है। गुणनफल के लिए \(\frac{c}{a}\) का प्रयोग करें।
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समीकरण \(5x^2-3x-11=0\) में मूलों का गुणनफल क्या है?
What is the product of roots of \(5x^2-3x-11=0\)?
#quadratic-equations
#product-of-roots
#medium
A \(-\frac{11}{5}\)
B \(\frac{11}{5}\)
C \(-\frac{3}{5}\)
D \(\frac{3}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{11}{5}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-11}{5}\). The sign of (c) is used directly in the formula.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{11}{5}\). The product of roots is \(\frac{c}{a}=\frac{-11}{5}\). The sign of (c) is used directly in the formula.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-11}{5}\) है। (c) का चिन्ह सूत्र में सीधे आता है।
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यदि \(kx^2-4x+2=0\) में मूलों का गुणनफल (1) है, तो (k) का मान क्या है?
If the product of roots of \(kx^2-4x+2=0\) is (1), what is the value of (k)?
#quadratic-equations
#parameter
#product-of-roots
#medium
A (1)
B (2)
C (-2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{2}{k}=1\), so (k=2). Use (c/a) for the product formula.
Step 2
Why this answer is correct
The correct answer is B. (2). The product of roots is \(\frac{2}{k}=1\), so (k=2). Use (c/a) for the product formula.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{2}{k}=1\), इसलिए (k=2) है। गुणनफल के सूत्र में (c/a) प्रयोग करें।
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समीकरण \(3x^2+2x-8=0\) में मूलों का गुणनफल क्या है?
What is the product of roots of \(3x^2+2x-8=0\)?
#quadratic-equations
#product-of-roots
#medium
A \(-\frac{8}{3}\)
B \(\frac{8}{3}\)
C \(-\frac{2}{3}\)
D \(\frac{2}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{8}{3}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-8}{3}\). Use the sign of (c) directly in the formula.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{8}{3}\). The product of roots is \(\frac{c}{a}=\frac{-8}{3}\). Use the sign of (c) directly in the formula.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-8}{3}\) है। (c) का चिन्ह सीधे सूत्र में रखें।
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कौन-सा विकल्प \(\sqrt{a}\times\sqrt{b}\) को परिमेय बनाने के लिए सही उदाहरण है?
Which option is a correct example that makes \(\sqrt{a}\times\sqrt{b}\) rational?
#product of roots
#perfect square
#class 10
A (a=2,b=7)
B (a=3,b=12)
C (a=5,b=6)
D (a=7,b=8)
Explanation opens after your attempt
Correct Answer
B. (a=3,b=12)
Step 1
Concept
\(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\).
Step 2
Why this answer is correct
For (a=3,b=12), (ab=36), so \(\sqrt{36}=6\), which is rational.
Step 3
Exam Tip
Check whether the product inside the radical becomes a perfect square. चरण 1: \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\) होता है। चरण 2: (a=3,b=12) पर (ab=36), इसलिए \(\sqrt{36}=6\), जो परिमेय है। चरण 3: गुणन के बाद अंदर की संख्या पूर्ण वर्ग बन रही है या नहीं, यह देखें।
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