यदि (p(x)=2x-2 -7x+5), तो शून्यकों के योग और गुणनफल का अंतर क्या है?
If (p(x)=2x-2 -7x+5), what is the difference between the sum and product of its zeroes?
#sum-product
#quadratic
#zeroes
A (1)
B (2)
C \(\frac{1}{2}\)
D (3)
Explanation opens after your attempt
Step 1
Concept
The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).
Step 2
Why this answer is correct
The correct answer is A. (1). The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).
Step 3
Exam Tip
योग \(\frac{7}{2}\) और गुणनफल \(\frac{5}{2}\) है। उनका अंतर \(\frac{7}{2}-\frac{5}{2}=1\) है।
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यदि (p(x)=x-2 -ax+a) के शून्यकों का गुणनफल और योग बराबर हैं, तो \(a\neq0\) होने पर (a) क्या है?
If the sum and product of zeroes of (p(x)=x-2 -ax+a) are equal, and \(a\neq0\), what is (a)?
#sum-product
#parameter
#conceptual
A कोई भी अशून्य वास्तविक संख्या / Any non-zero real number
B सिर्फ (1) / Only (1)
C सिर्फ (-1) / Only (-1)
D सिर्फ (2) / Only (2)
Explanation opens after your attempt
Correct Answer
A. कोई भी अशून्य वास्तविक संख्या / Any non-zero real number
Step 1
Concept
The sum is (a) and the product is also (a). Therefore every non-zero (a) works.
Step 2
Why this answer is correct
The correct answer is A. कोई भी अशून्य वास्तविक संख्या / Any non-zero real number. The sum is (a) and the product is also (a). Therefore every non-zero (a) works.
Step 3
Exam Tip
योग (a) और गुणनफल (a) दोनों समान हैं। इसलिए \(a\neq0\) के लिए हर अशून्य (a) काम करता है।
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यदि शून्यकों का योग (-4) और गुणनफल (7) है, तो मोनिक द्विघात बहुपद कौन-सा है?
If the sum of zeroes is (-4) and product is (7), which is the monic quadratic polynomial?
#sum-product
#construct-polynomial
#quadratic
A \(x^2+4x+7\)
B \(x^2-4x+7\)
C \(x^2+7x-4\)
D \(x^2-7x+4\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+7\)
Step 1
Concept
\(A monic quadratic is (x^2-(\)sum)x+product\(). Hence (x^2-(-4)x+7=x^2+4x+7).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+4x+7). A monic quadratic is (x^2-(\)sum)x+product\(). Hence (x^2-(-4)x+7=x^2+4x+7).\)
Step 3
Exam Tip
\(मोनिक द्विघात (x^2-(\)योग)x+गुणनफल) होता है। \(इसलिए (x^2-(-4)x+7=x^2+4x+7) है\)।
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दो धनात्मक संख्याओं का योग (19) और गुणनफल (84) है। वे संख्याएँ कौन सी हैं?
The sum of two positive numbers is (19) and their product is (84). Which numbers are they?
#quadratic equations
#sum product
#number problem
A (6) और (13) / (6) and (13)
B (7) और (12) / (7) and (12)
C (8) और (11) / (8) and (11)
D (9) और (10) / (9) and (10)
Explanation opens after your attempt
Correct Answer
B. (7) और (12) / (7) and (12)
Step 1
Concept
If one number is (x), the other is (19-x). From (x(19-x)=84), we get (7) and (12).
Step 2
Why this answer is correct
The correct answer is B. (7) और (12) / (7) and (12). If one number is (x), the other is (19-x). From (x(19-x)=84), we get (7) and (12).
Step 3
Exam Tip
यदि एक संख्या (x) है तो दूसरी (19-x) है। (x(19-x)=84) से (7) और (12) मिलते हैं।
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दो धनात्मक संख्याओं का योग (21) है और उनका गुणनफल (108) है। बड़ी संख्या क्या है?
The sum of two positive numbers is (21), and their product is (108). What is the larger number?
#quadratic equations
#sum product
#number problem
A (9)
B (10)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let the numbers be (x) and (21-x), then (x(21-x)=108). The roots are (9) and (12), so the larger number is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). Let the numbers be (x) and (21-x), then (x(21-x)=108). The roots are (9) and (12), so the larger number is (12).
Step 3
Exam Tip
संख्याएँ (x) और (21-x) हों, तो (x(21-x)=108)। मूल (9) और (12) हैं, इसलिए बड़ी संख्या (12) है।
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दो संख्याओं का योग (29) है और गुणनफल (204) है। बड़ी संख्या क्या है?
The sum of two numbers is (29) and their product is (204). What is the larger number?
#quadratic-equations
#word-problems
#sum-product
A (17)
B (12)
C (15)
D (29)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (29-x). From (x(29-x)=204), the numbers are (17) and (12).
Step 2
Why this answer is correct
The correct answer is A. (17). If one number is (x), the other is (29-x). From (x(29-x)=204), the numbers are (17) and (12).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (29-x) होगी। (x(29-x)=204) से संख्याएँ (17) और (12) मिलती हैं।
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दो संख्याओं का योग (15) है और गुणनफल (54) है। बड़ी संख्या क्या है?
The sum of two numbers is (15) and their product is (54). What is the larger number?
#quadratic-equations
#word-problems
#sum-product
A (9)
B (6)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
If one number is (x), the other is (15-x). From (x(15-x)=54), the numbers are (9) and (6).
Step 2
Why this answer is correct
The correct answer is A. (9). If one number is (x), the other is (15-x). From (x(15-x)=54), the numbers are (9) and (6).
Step 3
Exam Tip
यदि एक संख्या (x) है, तो दूसरी (15-x) होगी। (x(15-x)=54) से संख्याएँ (9) और (6) मिलती हैं।
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दो संख्याओं का योग (47) है और गुणनफल (540) है। बड़ी संख्या क्या है?
The sum of two numbers is (47) and their product is (540). What is the larger number?
#quadratic equations
#sum product
#application
A (20)
B (22)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
If the numbers are (x) and (47-x), then (x(47-x)=540). The solutions are (20) and (27), so the larger number is (27).
Step 2
Why this answer is correct
The correct answer is D. (27). If the numbers are (x) and (47-x), then (x(47-x)=540). The solutions are (20) and (27), so the larger number is (27).
Step 3
Exam Tip
संख्याएँ (x) और (47-x) हों तो (x(47-x)=540) है। हल (20) और (27) हैं, इसलिए बड़ी संख्या (27) है।
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दो संख्याओं का योग (43) है और गुणनफल (460) है। छोटी संख्या क्या है?
The sum of two numbers is (43) and their product is (460). What is the smaller number?
#quadratic equations
#sum product
#number problem
A (18)
B (20)
C (23)
D (25)
Explanation opens after your attempt
Step 1
Concept
Take the numbers as (x) and (43-x). From (x(43-x)=460), the numbers are (20) and (23), so the smaller number is (20).
Step 2
Why this answer is correct
The correct answer is B. (20). Take the numbers as (x) and (43-x). From (x(43-x)=460), the numbers are (20) and (23), so the smaller number is (20).
Step 3
Exam Tip
संख्याएँ (x) और (43-x) लें। (x(43-x)=460) से (20) और (23) मिलते हैं, इसलिए छोटी संख्या (20) है।
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दो संख्याओं का योग (31) है और गुणनफल (238) है। बड़ी संख्या क्या है?
The sum of two numbers is (31) and their product is (238). What is the larger number?
#quadratic equations
#sum product
#application
A (13)
B (14)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
(x(31-x)=238) gives the numbers (14) and (17). Hence the larger number is (17).
Step 2
Why this answer is correct
The correct answer is C. (17). (x(31-x)=238) gives the numbers (14) and (17). Hence the larger number is (17).
Step 3
Exam Tip
(x(31-x)=238) से संख्याएँ (14) और (17) हैं। इसलिए बड़ी संख्या (17) है।
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दो संख्याओं का योग (29) है और गुणनफल (204) है। छोटी संख्या क्या है?
The sum of two numbers is (29) and their product is (204). What is the smaller number?
#quadratic equations
#sum product
#number problem
A (10)
B (12)
C (17)
D (19)
Explanation opens after your attempt
Step 1
Concept
If the numbers are (x) and (29-x), then (x(29-x)=204) gives (12) and (17). The smaller number is (12).
Step 2
Why this answer is correct
The correct answer is B. (12). If the numbers are (x) and (29-x), then (x(29-x)=204) gives (12) and (17). The smaller number is (12).
Step 3
Exam Tip
संख्याएँ (x) और (29-x) हों, तब (x(29-x)=204) से (12) और (17) मिलते हैं। छोटी संख्या (12) है।
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दो संख्याओं का योग (25) है और गुणनफल (156) है। बड़ी संख्या क्या है?
The sum of two numbers is (25) and their product is (156). What is the larger number?
#quadratic equations
#sum product
#number problem
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
(x(25-x)=156) gives the numbers (12) and (13). Therefore, the larger number is (13).
Step 2
Why this answer is correct
The correct answer is B. (13). (x(25-x)=156) gives the numbers (12) and (13). Therefore, the larger number is (13).
Step 3
Exam Tip
(x(25-x)=156) से संख्याएँ (12) और (13) हैं। इसलिए बड़ी संख्या (13) है।
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दो संख्याओं का योग (21) है और गुणनफल (110) है। छोटी संख्या क्या है?
The sum of two numbers is (21) and their product is (110). What is the smaller number?
#quadratic equations
#sum product
#application
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
If the numbers are (x) and (21-x), then (x(21-x)=110) gives (10) and (11). The smaller number is (10).
Step 2
Why this answer is correct
The correct answer is B. (10). If the numbers are (x) and (21-x), then (x(21-x)=110) gives (10) and (11). The smaller number is (10).
Step 3
Exam Tip
संख्याएँ (x) और (21-x) हों, तब (x(21-x)=110) से (10) और (11) मिलते हैं। छोटी संख्या (10) है।
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दो संख्याओं का योग (19) है और गुणनफल (90) है। बड़ी संख्या क्या है?
The sum of two numbers is (19) and their product is (90). What is the larger number?
#quadratic equations
#sum product
#application
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
Putting the numbers as (x) and (19-x), (x(19-x)=90). The solutions are (9) and (10), so the larger number is (10).
Step 2
Why this answer is correct
The correct answer is B. (10). Putting the numbers as (x) and (19-x), (x(19-x)=90). The solutions are (9) and (10), so the larger number is (10).
Step 3
Exam Tip
संख्याएँ (x) और (19-x) रखने पर (x(19-x)=90) बनता है। हल (9) और (10) हैं, इसलिए बड़ी संख्या (10) है।
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दो संख्याओं का योग (17) है और गुणनफल (72) है। छोटी संख्या क्या है?
The sum of two numbers is (17) and their product is (72). What is the smaller number?
#quadratic equations
#sum product
#number problem
A (6)
B (8)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
Take the numbers as (x) and (17-x), then (x(17-x)=72) gives (8) and (9). The smaller number is (8).
Step 2
Why this answer is correct
The correct answer is B. (8). Take the numbers as (x) and (17-x), then (x(17-x)=72) gives (8) and (9). The smaller number is (8).
Step 3
Exam Tip
संख्याएँ (x) और (17-x) लें, तब (x(17-x)=72) से संख्याएँ (8) और (9) हैं। छोटी संख्या (8) है।
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यदि \(x^2-6x+c=0\) की जड़ें \(\alpha,\beta\) हैं और \(\alpha^2+\beta^2=26\), तो जड़ें क्या हैं?
If \(\alpha,\beta\) are roots of \(x^2-6x+c=0\) and \(\alpha^2+\beta^2=26\), what are the roots?
#quadratic-roots
#determine-roots
#sum-product
A (1) और (5) / (1) and (5)
B (2) और (4) / (2) and (4)
C (3) और (3) / (3) and (3)
D (0) और (6) / (0) and (6)
Explanation opens after your attempt
Correct Answer
A. (1) और (5) / (1) and (5)
Step 1
Concept
Here \(\alpha+\beta=6\) and \(\alpha^2+\beta^2=26\). From \(36-2\alpha\beta=26\), \(\alpha\beta=5\), so the roots are (1) and (5).
Step 2
Why this answer is correct
The correct answer is A. (1) और (5) / (1) and (5). Here \(\alpha+\beta=6\) and \(\alpha^2+\beta^2=26\). From \(36-2\alpha\beta=26\), \(\alpha\beta=5\), so the roots are (1) and (5).
Step 3
Exam Tip
\(\alpha+\beta=6\) और \(\alpha^2+\beta^2=26\) है। \(36-2\alpha\beta=26\) से \(\alpha\beta=5\), इसलिए जड़ें (1) और (5) हैं।
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यदि \(x^2-7x+10=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^2-6\alpha+\beta^2-6\beta\) का सही मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-7x+10=0\), what is the correct value of \(\alpha^2-6\alpha+\beta^2-6\beta\)?
#quadratic-roots
#root-expression
#sum-product
A (-13)
B (-11)
C (-9)
D (-7)
Explanation opens after your attempt
Step 1
Concept
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=49-20=29). Therefore the value is (29-6\(\alpha+\beta\)=29-42=-13).
Step 2
Why this answer is correct
The correct answer is A. (-13). (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=49-20=29). Therefore the value is (29-6\(\alpha+\beta\)=29-42=-13).
Step 3
Exam Tip
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=49-20=29) है। इसलिए मान (29-6\(\alpha+\beta\)=29-42=-13) है।
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(x-2 -(u+2v)x+2uv=0) की जड़ें कौन-सी हैं?
What are the roots of (x-2 -(u+2v)x+2uv=0)?
#quadratic-roots
#general-roots
#sum-product
A (u) और (2v) / (u) and (2v)
B (2u) और (v) / (2u) and (v)
C (u+v) और (v) / (u+v) and (v)
D (-u) और (-2v) / (-u) and (-2v)
Explanation opens after your attempt
Correct Answer
A. (u) और (2v) / (u) and (2v)
Step 1
Concept
The sum of roots is (u+2v) and the product is (2uv). These match (u) and (2v).
Step 2
Why this answer is correct
The correct answer is A. (u) और (2v) / (u) and (2v). The sum of roots is (u+2v) and the product is (2uv). These match (u) and (2v).
Step 3
Exam Tip
जड़ों का योग (u+2v) और गुणनफल (2uv) है। ये (u) और (2v) से मेल खाते हैं।
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यदि \(x^2-13x+36=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?
If \(\alpha,\beta\) are the roots of \(x^2-13x+36=0\), what is \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)?
#quadratic-roots
#ratio-expression
#sum-product
A \(\frac{97}{36}\)
B \(\frac{101}{36}\)
C \(\frac{105}{36}\)
D \(\frac{109}{36}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{97}{36}\)
Step 1
Concept
We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha^2+\beta^2=169-72=97\) and \(\alpha\beta=36\), so the value is \(\frac{97}{36}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{97}{36}\). We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha^2+\beta^2=169-72=97\) and \(\alpha\beta=36\), so the value is \(\frac{97}{36}\).
Step 3
Exam Tip
\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\) है। यहाँ \(\alpha^2+\beta^2=169-72=97\) और \(\alpha\beta=36\), इसलिए मान \(\frac{97}{36}\) है।
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(x-2 -2(a+2)x+a-2 +4a=0) की जड़ें कौन-सी हैं?
What are the roots of (x-2 -2(a+2)x+a-2 +4a=0)?
#quadratic-roots
#parametric-roots
#sum-product
A (a) और (a+4) / (a) and (a+4)
B (a+2) और (a+2) / (a+2) and (a+2)
C (a-2) और (a+2) / (a-2) and (a+2)
D (2a) और (4) / (2a) and (4)
Explanation opens after your attempt
Correct Answer
A. (a) और (a+4) / (a) and (a+4)
Step 1
Concept
The sum of roots is (2a+4) and the product is \(a^2+4a\). These match (a) and (a+4).
Step 2
Why this answer is correct
The correct answer is A. (a) और (a+4) / (a) and (a+4). The sum of roots is (2a+4) and the product is \(a^2+4a\). These match (a) and (a+4).
Step 3
Exam Tip
जड़ों का योग (2a+4) और गुणनफल \(a^2+4a\) है। ये (a) और (a+4) से मेल खाते हैं।
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यदि \(x^2-4x-12=0\) की जड़ें \(\alpha,\beta\) हैं, तो (\(\alpha-5\)\(\beta-5\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-4x-12=0\), what is (\(\alpha-5\)\(\beta-5\))?
#quadratic-roots
#root-expression
#sum-product
A (-7)
B (-5)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
We use (\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25). Since \(\alpha+\beta=4\) and \(\alpha\beta=-12\), the value is (-7).
Step 2
Why this answer is correct
The correct answer is A. (-7). We use (\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25). Since \(\alpha+\beta=4\) and \(\alpha\beta=-12\), the value is (-7).
Step 3
Exam Tip
(\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25) है। \(\alpha+\beta=4\) और \(\alpha\beta=-12\), इसलिए मान (-7) है।
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यदि किसी द्विघात समीकरण की जड़ों का योग (7) और गुणनफल (10) है, तो समीकरण कौन-सा है?
If the sum of roots of a quadratic equation is (7) and the product is (10), which is the equation?
#quadratic-roots
#forming-equation
#sum-product
A \(x^2+7x+10=0\)
B \(x^2-10x+7=0\)
C \(x^2-7x+10=0\)
D \(x^2+10x-7=0\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-7x+10=0\)
Step 1
Concept
\(The equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-7x+10=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is C. (x^2-7x+10=0). The equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-7x+10=0) is correct.\)
Step 3
Exam Tip
\(जड़ों का समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-7x+10=0) सही है\)।
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यदि \(x^2-5x+c=0\) की जड़ें \(\alpha,\beta\) हैं और \(\alpha^2+\beta^2=17\), तो जड़ें क्या हैं?
If \(\alpha,\beta\) are roots of \(x^2-5x+c=0\) and \(\alpha^2+\beta^2=17\), what are the roots?
#quadratic-roots
#determine-roots
#sum-product
A (1) और (4) / (1) and (4)
B (2) और (3) / (2) and (3)
C (0) और (5) / (0) and (5)
D (-1) और (6) / (-1) and (6)
Explanation opens after your attempt
Correct Answer
A. (1) और (4) / (1) and (4)
Step 1
Concept
Here \(\alpha+\beta=5\) and \(\alpha^2+\beta^2=17\). From \(25-2\alpha\beta=17\), \(\alpha\beta=4\), so the roots are (1) and (4).
Step 2
Why this answer is correct
The correct answer is A. (1) और (4) / (1) and (4). Here \(\alpha+\beta=5\) and \(\alpha^2+\beta^2=17\). From \(25-2\alpha\beta=17\), \(\alpha\beta=4\), so the roots are (1) and (4).
Step 3
Exam Tip
\(\alpha+\beta=5\) और \(\alpha^2+\beta^2=17\) है। \(25-2\alpha\beta=17\) से \(\alpha\beta=4\), इसलिए जड़ें (1) और (4) हैं।
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यदि \(x^2+8x+12=0\) की जड़ें \(\alpha,\beta\) हैं, तो (\(\alpha-\beta\)2 +3\alpha\beta) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2+8x+12=0\), what is (\(\alpha-\beta\)2 +3\alpha\beta)?
#quadratic-roots
#difference-expression
#sum-product
A (48)
B (50)
C (52)
D (56)
Explanation opens after your attempt
Step 1
Concept
Here (\(\alpha-\beta\)2 =\(\alpha+\beta\)2 -4\alpha\beta=64-48=16). Therefore (16+3(12)=52).
Step 2
Why this answer is correct
The correct answer is C. (52). Here (\(\alpha-\beta\)2 =\(\alpha+\beta\)2 -4\alpha\beta=64-48=16). Therefore (16+3(12)=52).
Step 3
Exam Tip
(\(\alpha-\beta\)2 =\(\alpha+\beta\)2 -4\alpha\beta=64-48=16) है। इसलिए (16+3(12)=52)।
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यदि \(x^2-6x+5=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^2-5\alpha+\beta^2-5\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-6x+5=0\), what is \(\alpha^2-5\alpha+\beta^2-5\beta\)?
#quadratic-roots
#root-expression
#sum-product
A (-6)
B (-4)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=6\) and \(\alpha\beta=5\). Since \(\alpha^2+\beta^2=26\), the value is (26-5\(\alpha+\beta\)=-4).
Step 2
Why this answer is correct
The correct answer is B. (-4). Here \(\alpha+\beta=6\) and \(\alpha\beta=5\). Since \(\alpha^2+\beta^2=26\), the value is (26-5\(\alpha+\beta\)=-4).
Step 3
Exam Tip
\(\alpha+\beta=6\) और \(\alpha\beta=5\) है। \(\alpha^2+\beta^2=26\), इसलिए (26-5\(\alpha+\beta\)=-4)।
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(x-2 -(u-v)x-uv=0) की जड़ें कौन-सी हैं?
What are the roots of (x-2 -(u-v)x-uv=0)?
#quadratic-roots
#general-roots
#sum-product
A (u) और (v) / (u) and (v)
B (u) और (-v) / (u) and (-v)
C (-u) और (v) / (-u) and (v)
D (u-v) और (uv) / (u-v) and (uv)
Explanation opens after your attempt
Correct Answer
B. (u) और (-v) / (u) and (-v)
Step 1
Concept
The sum of roots is (u-v) and the product is (-uv). These match (u) and (-v).
Step 2
Why this answer is correct
The correct answer is B. (u) और (-v) / (u) and (-v). The sum of roots is (u-v) and the product is (-uv). These match (u) and (-v).
Step 3
Exam Tip
जड़ों का योग (u-v) और गुणनफल (-uv) है। ये (u) और (-v) से मेल खाते हैं।
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यदि \(x^2-11x+24=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?
If \(\alpha,\beta\) are the roots of \(x^2-11x+24=0\), what is \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)?
#quadratic-roots
#ratio-expression
#sum-product
A \(\frac{61}{24}\)
B \(\frac{67}{24}\)
C \(\frac{73}{24}\)
D \(\frac{79}{24}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{73}{24}\)
Step 1
Concept
We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha^2+\beta^2=73\) and \(\alpha\beta=24\), so the value is \(\frac{73}{24}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{73}{24}\). We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha^2+\beta^2=73\) and \(\alpha\beta=24\), so the value is \(\frac{73}{24}\).
Step 3
Exam Tip
\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\) है। यहाँ \(\alpha^2+\beta^2=73\) और \(\alpha\beta=24\), इसलिए मान \(\frac{73}{24}\) है।
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(x-2 -2(a+1)x+a-2 +2a=0) की जड़ें कौन-सी हैं?
What are the roots of (x-2 -2(a+1)x+a-2 +2a=0)?
#quadratic-roots
#parametric-roots
#sum-product
A (a) और (a+2) / (a) and (a+2)
B (a+1) और (a+1) / (a+1) and (a+1)
C (2a) और (2) / (2a) and (2)
D (a-2) और (a+2) / (a-2) and (a+2)
Explanation opens after your attempt
Correct Answer
A. (a) और (a+2) / (a) and (a+2)
Step 1
Concept
The sum of roots is (2a+2) and the product is \(a^2+2a\). These match (a) and (a+2).
Step 2
Why this answer is correct
The correct answer is A. (a) और (a+2) / (a) and (a+2). The sum of roots is (2a+2) and the product is \(a^2+2a\). These match (a) and (a+2).
Step 3
Exam Tip
जड़ों का योग (2a+2) और गुणनफल \(a^2+2a\) है। ये (a) और (a+2) से मिलते हैं।
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यदि \(x^2-3x-10=0\) की जड़ें \(\alpha,\beta\) हैं, तो (\(\alpha-4\)\(\beta-4\)) का मान क्या है?
If \(\alpha,\beta\) are the roots of \(x^2-3x-10=0\), what is (\(\alpha-4\)\(\beta-4\))?
#quadratic-roots
#root-expression
#sum-product
A (-10)
B (-8)
C (-6)
D (6)
Explanation opens after your attempt
Step 1
Concept
We use (\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Since \(\alpha+\beta=3\) and \(\alpha\beta=-10\), the value is (-6).
Step 2
Why this answer is correct
The correct answer is C. (-6). We use (\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Since \(\alpha+\beta=3\) and \(\alpha\beta=-10\), the value is (-6).
Step 3
Exam Tip
(\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16) है। \(\alpha+\beta=3\) और \(\alpha\beta=-10\), इसलिए मान (-6) है।
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यदि \(x^2-4x+c=0\) की जड़ें \(\alpha,\beta\) हैं और \(\alpha^2+\beta^2=10\), तो समीकरण की जड़ें क्या हैं?
If \(\alpha,\beta\) are roots of \(x^2-4x+c=0\) and \(\alpha^2+\beta^2=10\), what are the roots of the equation?
#quadratic-roots
#determine-roots
#sum-product
A (1) और (3) / (1) and (3)
B (2) और (2) / (2) and (2)
C (0) और (4) / (0) and (4)
D (-1) और (5) / (-1) and (5)
Explanation opens after your attempt
Correct Answer
A. (1) और (3) / (1) and (3)
Step 1
Concept
Here \(\alpha+\beta=4\) and \(\alpha^2+\beta^2=10\). From \(16-2\alpha\beta=10\), \(\alpha\beta=3\), so the roots are (1) and (3).
Step 2
Why this answer is correct
The correct answer is A. (1) और (3) / (1) and (3). Here \(\alpha+\beta=4\) and \(\alpha^2+\beta^2=10\). From \(16-2\alpha\beta=10\), \(\alpha\beta=3\), so the roots are (1) and (3).
Step 3
Exam Tip
\(\alpha+\beta=4\) और \(\alpha^2+\beta^2=10\) है। \(16-2\alpha\beta=10\) से \(\alpha\beta=3\), इसलिए जड़ें (1) और (3) हैं।
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