एक समांतर श्रेढ़ी में (a=9), (d=6) है। यदि \(S_n=525\), तो (n) का मान क्या होगा?
In an AP, (a=9) and (d=6). If \(S_n=525\), what is the value of (n)?
#find n
#quadratic
#ap sum
A (10)
B (12)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
Solving (\frac{n}{2}[18+6(n-1)]=525) gives (n=10). For (n), a quadratic may appear, so choose the positive value.
Step 2
Why this answer is correct
The correct answer is A. (10). Solving (\frac{n}{2}[18+6(n-1)]=525) gives (n=10). For (n), a quadratic may appear, so choose the positive value.
Step 3
Exam Tip
(\frac{n}{2}[18+6(n-1)]=525) हल करने पर (n=10) मिलता है। (n) के लिए द्विघात बन सकता है, सही धनात्मक मान चुनें।
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यदि (p(x)=x-2 +px+q) और (p(1)=0,\ p(2)=0), तो (p+q) क्या है?
If (p(x)=x-2 +px+q) and (p(1)=0,\ p(2)=0), what is (p+q)?
#coefficient-finding
#zeroes
#quadratic
A -(1)
B (1)
C -(2)
D (2)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).
Step 2
Why this answer is correct
The correct answer is A. -(1). The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).
Step 3
Exam Tip
शून्यक (1) और (2) हैं, इसलिए बहुपद \(x^2-3x+2\) है। अतः (p=-3,\ q=2) और (p+q=-1)।
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यदि (p(x)=x-2 -6x+8), तो शून्यकों के वर्गों से बना मोनिक बहुपद कौन-सा है?
If (p(x)=x-2 -6x+8), which monic polynomial has the squares of its zeroes as zeroes?
#transformed-zeroes
#squares
#quadratic
A \(x^2-20x+64\)
B \(x^2-6x+8\)
C \(x^2-12x+16\)
D \(x^2-16x+64\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-20x+64\)
Step 1
Concept
The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-20x+64\). The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).
Step 3
Exam Tip
मूल शून्यक (2) और (4) हैं, इसलिए नए शून्यक (4) और (16) हैं। नया बहुपद \(x^2-20x+64\) है।
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यदि (p(x)=x-2 -7x+12) है, तो (p(x)) का ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?
If (p(x)=x-2 -7x+12), at which points will the graph of (p(x)) cut the (x)-axis?
#graph-zeroes
#quadratic
#intercepts
A ((3,0),(4,0))
B ((0,3),(0,4))
C ((2,0),(6,0))
D ((0,0),(7,0))
Explanation opens after your attempt
Correct Answer
A. ((3,0),(4,0))
Step 1
Concept
(x-2 -7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).
Step 2
Why this answer is correct
The correct answer is A. ((3,0),(4,0)). (x-2 -7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).
Step 3
Exam Tip
(x-2 -7x+12=(x-3)(x-4)), इसलिए शून्यक (3) और (4) हैं। (x)-अक्ष पर बिंदु ((3,0)) और ((4,0)) होंगे।
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यदि (p(x)=x-2 +5x+6) और (r(x)=p(-x)), तो (r(x)) के शून्यक कौन-से हैं?
If (p(x)=x-2 +5x+6) and (r(x)=p(-x)), what are the zeroes of (r(x))?
#transformed-zeroes
#reflection
#quadratic
A (2,3)
B -(2,-3)
C (1,6)
D -(1,-6)
Explanation opens after your attempt
Step 1
Concept
The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).
Step 2
Why this answer is correct
The correct answer is A. (2,3). The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).
Step 3
Exam Tip
(p(x)) के शून्यक (-2) और (-3) हैं। (p(-x)=0) के लिए (-x=-2) या (-x=-3), इसलिए (x=2,3)।
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यदि (p(x)=x-2 -4x+3) है, तो कौन-सा मान (p(x)<0) बनाता है?
If (p(x)=x-2 -4x+3), which value makes (p(x)<0)?
#sign-of-polynomial
#quadratic
#zeroes
A (2)
B (0)
C (4)
D -(1)
Explanation opens after your attempt
Step 1
Concept
(p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.
Step 3
Exam Tip
(p(x)=(x-1)(x-3)) है और (1<x<3) में मान ऋणात्मक होता है। इसलिए (x=2) सही है।
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यदि (p(x)=x-2 -2x+k) का न्यूनतम मान (3) है, तो (k) क्या है?
If the minimum value of (p(x)=x-2 -2x+k) is (3), what is (k)?
#complete-square
#minimum-value
#quadratic
A (4)
B (3)
C (2)
D (1)
Explanation opens after your attempt
Step 1
Concept
(x-2 -2x+k=(x-1)2 +k-1), so the minimum value is (k-1). From (k-1=3), (k=4).
Step 2
Why this answer is correct
The correct answer is A. (4). (x-2 -2x+k=(x-1)2 +k-1), so the minimum value is (k-1). From (k-1=3), (k=4).
Step 3
Exam Tip
(x-2 -2x+k=(x-1)2 +k-1), इसलिए न्यूनतम मान (k-1) है। (k-1=3) से (k=4)।
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यदि (p(x)=5x-2 -20x+20), तो इसके शून्यकों का योग क्या है?
If (p(x)=5x-2 -20x+20), what is the sum of its zeroes?
#sum-zeroes
#quadratic
#formula
A (4)
B (5)
C -(4)
D (2)
Explanation opens after your attempt
Step 1
Concept
The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.
Step 2
Why this answer is correct
The correct answer is A. (4). The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.
Step 3
Exam Tip
योग \(-\frac{b}{a}=-\frac{-20}{5}=4\) है। पहले सामान्य गुणनखंड निकालना चाहें तो भी योग वही रहेगा।
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यदि (p(x)=x-2 +2x-24), तो (p(x)) का कौन-सा गुणनखंड है?
If (p(x)=x-2 +2x-24), which is a factor of (p(x))?
#factorisation
#quadratic
#polynomial
A (x-4)
B (x+4)
C (x-6)
D (x+2)
Explanation opens after your attempt
Step 1
Concept
(x-2 +2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.
Step 2
Why this answer is correct
The correct answer is A. (x-4). (x-2 +2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.
Step 3
Exam Tip
(x-2 +2x-24=(x-4)(x+6)) है। इसलिए (x-4) एक गुणनखंड है।
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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 -kx+36) के शून्यक धनात्मक और अनुपात (1:4) में हैं, तो (k) क्या है?
If the zeroes of (p(x)=x-2 -kx+36) are positive and in the ratio (1:4), what is (k)?
#ratio-zeroes
#parameter
#quadratic
A (15)
B (12)
C (9)
D (18)
Explanation opens after your attempt
Step 1
Concept
Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).
Step 2
Why this answer is correct
The correct answer is A. (15). Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).
Step 3
Exam Tip
शून्यक (t) और (4t) मानें, तो \(4t^2=36\) से (t=3) है। योग (15) है, इसलिए (k=15)।
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यदि (p(x)=x-2 -5x+6), तो (p(2)+p(3)) का मान क्या है?
If (p(x)=x-2 -5x+6), what is the value of (p(2)+p(3))?
#evaluation
#zeroes
#quadratic
A (0)
B (1)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). (2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).
Step 3
Exam Tip
(2) और (3), (p(x)) के शून्यक हैं, इसलिए (p(2)=0) और (p(3)=0)। इसलिए योग (0) है।
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यदि (p(x)=x-2 -2x-8), तो (p(x+3)) के शून्यक कौन-से हैं?
If (p(x)=x-2 -2x-8), what are the zeroes of (p(x+3))?
#transformed-zeroes
#quadratic
#expert
A -(5,1)
B -(1,5)
C (2,-4)
D -(3,3)
Explanation opens after your attempt
Step 1
Concept
The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).
Step 2
Why this answer is correct
The correct answer is A. -(5,1). The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).
Step 3
Exam Tip
(p(x)) के शून्यक (4) और (-2) हैं। (x+3=4) या (x+3=-2) से शून्यक (1) और (-5) मिलते हैं।
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यदि (p(x)=4x-2 -4x+1), तो इसके शून्यक क्या हैं?
If (p(x)=4x-2 -4x+1), what are its zeroes?
#equal-zeroes
#perfect-square
#quadratic
A \(\frac{1}{2},\frac{1}{2}\)
B (1,1)
C -\(\frac{1}{2},-\frac{1}{2}\)
D (2,2)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2},\frac{1}{2}\)
Step 1
Concept
(4x-2 -4x+1=(2x-1)2 ), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2},\frac{1}{2}\). (4x-2 -4x+1=(2x-1)2 ), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.
Step 3
Exam Tip
(4x-2 -4x+1=(2x-1)2 ), इसलिए शून्यक \(\frac{1}{2}\) दो बार है। पूर्ण वर्ग रूप तुरंत समान शून्यक देता है।
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यदि (p(x)=2x-2 +mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=2x-2 +mx+18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A (3)
B -(3)
C (6)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 3
Exam Tip
गुणनफल \(\frac{18}{2}=9\) है। एक शून्यक (3) है, इसलिए दूसरा (3) होगा।
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यदि (p(x)=3x-2 -12x+15), तो वास्तविक शून्यकों के बारे में सही निष्कर्ष क्या है?
For (p(x)=3x-2 -12x+15), what is the correct conclusion about real zeroes?
#real-zeroes
#complete-square
#quadratic
A कोई वास्तविक शून्यक नहीं / No real zeroes
B दो समान वास्तविक शून्यक / Two equal real zeroes
C दो भिन्न वास्तविक शून्यक / Two distinct real zeroes
D एक शून्यक (5) / One zero (5)
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक शून्यक नहीं / No real zeroes
Step 1
Concept
(p(x)=3\(x^2-4x+5\)=3((x-2)2 +1)), which is always positive. Hence there are no real zeroes.
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक शून्यक नहीं / No real zeroes. (p(x)=3\(x^2-4x+5\)=3((x-2)2 +1)), which is always positive. Hence there are no real zeroes.
Step 3
Exam Tip
(p(x)=3\(x^2-4x+5\)=3((x-2)2 +1)), जो सदा धनात्मक है। इसलिए कोई वास्तविक शून्यक नहीं है।
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यदि किसी द्विघात बहुपद के शून्यक \(2+\sqrt{3}\) और \(2-\sqrt{3}\) हैं, तो मोनिक बहुपद कौन-सा है?
If the zeroes of a quadratic polynomial are \(2+\sqrt{3}\) and \(2-\sqrt{3}\), which is the monic polynomial?
#construct-polynomial
#surd-zeroes
#quadratic
A \(x^2-4x+1\)
B \(x^2+4x+1\)
C \(x^2-2x+3\)
D \(x^2-4x+7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x+1\)
Step 1
Concept
The sum is (4) and the product is (1). Therefore the monic polynomial is \(x^2-4x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+1\). The sum is (4) and the product is (1). Therefore the monic polynomial is \(x^2-4x+1\).
Step 3
Exam Tip
योग (4) और गुणनफल (1) है। अतः मोनिक बहुपद \(x^2-4x+1\) होगा।
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यदि (p(x)=x-2 -4x+1), तो शून्यकों के व्युत्क्रमों का योग क्या है?
If (p(x)=x-2 -4x+1), what is the sum of reciprocals of its zeroes?
#reciprocal-zeroes
#quadratic
#formula
A (4)
B (1)
C (-4)
D \(\frac{1}{4}\)
Explanation opens after your attempt
Step 1
Concept
The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).
Step 3
Exam Tip
शून्यकों के व्युत्क्रमों का योग \(\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=4\) और \(\alpha\beta=1\), इसलिए उत्तर (4) है।
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यदि \(\alpha,\beta\), \(x^2-9x+20\) के शून्यक हैं, तो (\(\alpha+2\)\(\beta+2\)) का मान क्या है?
If \(\alpha,\beta\) are zeroes of \(x^2-9x+20\), what is the value of (\(\alpha+2\)\(\beta+2\))?
#zeroes
#algebraic-expression
#quadratic
A (42)
B (38)
C (31)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(\alpha+\beta=9\) and \(\alpha\beta=20\). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42).
Step 2
Why this answer is correct
The correct answer is A. (42). \(\alpha+\beta=9\) and \(\alpha\beta=20\). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42).
Step 3
Exam Tip
\(\alpha+\beta=9\) और \(\alpha\beta=20\) हैं। (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42)।
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यदि (x=2) और (x=-3), (p(x)=ax-2 +bx+c) के शून्यक हैं, तो \(\frac{c}{a}\) क्या है?
If (x=2) and (x=-3) are zeroes of (p(x)=ax-2 +bx+c), what is \(\frac{c}{a}\)?
#zeroes
#coefficient-relation
#quadratic
A -(6)
B (6)
C -(1)
D (1)
Explanation opens after your attempt
Step 1
Concept
The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.
Step 2
Why this answer is correct
The correct answer is A. -(6). The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.
Step 3
Exam Tip
शून्यकों का गुणनफल (2\cdot(-3)=-6) है और यह \(\frac{c}{a}\) के बराबर होता है। गुणनफल में संकेत पर विशेष ध्यान दें।
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यदि \(\alpha\) और \(\beta\), \(3x^2-10x+7\) के शून्यक हैं, तो \(\alpha^2+\beta^2\) का मान क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(3x^2-10x+7\), what is the value of \(\alpha^2+\beta^2\)?
#zeroes
#identity
#quadratic
A \(\frac{58}{9}\)
B \(\frac{100}{9}\)
C \(\frac{14}{3}\)
D \(\frac{49}{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{58}{9}\)
Step 1
Concept
Here \(\alpha+\beta=\frac{10}{3}\) and \(\alpha\beta=\frac{7}{3}\). Hence (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9}).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{58}{9}\). Here \(\alpha+\beta=\frac{10}{3}\) and \(\alpha\beta=\frac{7}{3}\). Hence (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9}).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=\frac{10}{3}\) और \(\alpha\beta=\frac{7}{3}\) हैं। इसलिए (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9})।
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यदि (p(x)=x-2 +px+q), (p(0)=12) और (p(3)=0), तो (p) का मान क्या है?
If (p(x)=x-2 +px+q), (p(0)=12), and (p(3)=0), what is the value of (p)?
#parameter
#quadratic
#evaluation
A (-7)
B (-6)
C (-5)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(p(0)=q=12) and (p(3)=9+3p+12=0), so (3p=-21) and (p=-7). Find the constant term first.
Step 2
Why this answer is correct
The correct answer is A. (-7). (p(0)=q=12) and (p(3)=9+3p+12=0), so (3p=-21) and (p=-7). Find the constant term first.
Step 3
Exam Tip
(p(0)=q=12) और (p(3)=9+3p+12=0), इसलिए (3p=-21) और (p=-7)। पहले अचर पद निकालें।
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यदि (p(x)=x-2 +kx+25) पूर्ण वर्ग बहुपद है और (k<0), तो (k) क्या है?
If (p(x)=x-2 +kx+25) is a perfect square polynomial and (k<0), what is (k)?
#perfect square
#parameter
#quadratic
A (-10)
B (-5)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
For (x-2 +kx+25=(x-5)2 ), (k=-10). In a perfect square, the middle term is (2ab).
Step 2
Why this answer is correct
The correct answer is A. (-10). For (x-2 +kx+25=(x-5)2 ), (k=-10). In a perfect square, the middle term is (2ab).
Step 3
Exam Tip
(x-2 +kx+25=(x-5)2 ) होने पर (k=-10)। पूर्ण वर्ग में मध्य पद (2ab) होता है।
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(p(x)=x-2 +14x+53) का न्यूनतम मान क्या है?
What is the minimum value of (p(x)=x-2 +14x+53)?
#quadratic
#minimum
#value
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(x-2 +14x+53=(x+7)2 +4), so the minimum value is (4). A square term is never negative.
Step 2
Why this answer is correct
The correct answer is B. (4). (x-2 +14x+53=(x+7)2 +4), so the minimum value is (4). A square term is never negative.
Step 3
Exam Tip
(x-2 +14x+53=(x+7)2 +4), इसलिए न्यूनतम मान (4) है। वर्ग पद कभी ऋणात्मक नहीं होता।
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(p(x)=x-2 -12x+40) का न्यूनतम मान किस (x) पर आता है?
At which (x) does (p(x)=x-2 -12x+40) attain its minimum value?
#quadratic
#minimum
#completing square
A (x=4)
B (x=5)
C (x=6)
D (x=12)
Explanation opens after your attempt
Step 1
Concept
(x-2 -12x+40=(x-6)2 +4), so the minimum occurs at (x=6). Completing the square is useful.
Step 2
Why this answer is correct
The correct answer is C. (x=6). (x-2 -12x+40=(x-6)2 +4), so the minimum occurs at (x=6). Completing the square is useful.
Step 3
Exam Tip
(x-2 -12x+40=(x-6)2 +4), इसलिए न्यूनतम (x=6) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।
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(p(x)=16x-2 -24x+9) में कौन सा मान शून्य है?
Which value is a zero of (p(x)=16x-2 -24x+9)?
#zero
#fraction
#quadratic
A \(\frac{3}{4}\)
B \(-\frac{3}{4}\)
C \(\frac{4}{3}\)
D \(-\frac{4}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3}{4}\)
Step 1
Concept
(16x-2 -24x+9=(4x-3)2 ), so the zero is \(x=\frac{3}{4}\). Recognize the perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{4}\). (16x-2 -24x+9=(4x-3)2 ), so the zero is \(x=\frac{3}{4}\). Recognize the perfect square.
Step 3
Exam Tip
(16x-2 -24x+9=(4x-3)2 ), इसलिए शून्य \(x=\frac{3}{4}\) है। पूर्ण वर्ग पहचानें।
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(p(x)=x-2 -9x+20) में (p(4)+p(5)) का मान क्या है?
What is the value of (p(4)+p(5)) for (p(x)=x-2 -9x+20)?
#zeros
#evaluation
#quadratic
A (0)
B (1)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
(p(4)=0) and (p(5)=0), so the sum is (0). Both values are zeros of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(4)=0) and (p(5)=0), so the sum is (0). Both values are zeros of this polynomial.
Step 3
Exam Tip
(p(4)=0) और (p(5)=0), इसलिए योग (0) है। दोनों मान इस बहुपद के शून्य हैं।
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यदि (p(x)=x-2 +ax+b), (p(-4)=0) और (p(1)=0), तो (b) का मान क्या है?
If (p(x)=x-2 +ax+b), (p(-4)=0), and (p(1)=0), what is the value of (b)?
#zeros
#quadratic
#constant term
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
With zeros (-4) and (1), the polynomial is ((x+4)(x-1)=x-2 +3x-4). Hence (b=-4).
Step 2
Why this answer is correct
The correct answer is A. (-4). With zeros (-4) and (1), the polynomial is ((x+4)(x-1)=x-2 +3x-4). Hence (b=-4).
Step 3
Exam Tip
शून्य (-4) और (1) होने पर बहुपद ((x+4)(x-1)=x-2 +3x-4) है। इसलिए (b=-4)।
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यदि (p(x)=x-2 +ax+b), (p(-2)=0) और (p(5)=0), तो (a+b) क्या है?
If (p(x)=x-2 +ax+b), (p(-2)=0), and (p(5)=0), what is (a+b)?
#zeros
#quadratic
#parameter
A (-13)
B (-7)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
The zeros are (-2) and (5), so the polynomial is ((x+2)(x-5)=x-2 -3x-10). Hence (a+b=-3-10=-13).
Step 2
Why this answer is correct
The correct answer is A. (-13). The zeros are (-2) and (5), so the polynomial is ((x+2)(x-5)=x-2 -3x-10). Hence (a+b=-3-10=-13).
Step 3
Exam Tip
शून्य (-2) और (5) हैं, इसलिए बहुपद ((x+2)(x-5)=x-2 -3x-10) है। अतः (a+b=-3-10=-13)।
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यदि (x=-3), बहुपद (p(x)=x-2 +kx-18) का शून्य है, तो (k) क्या है?
If (x=-3) is a zero of (p(x)=x-2 +kx-18), what is (k)?
#zero
#parameter
#quadratic
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=9-3k-18=0), so (-3k=9) and (k=-3). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is A. (-3). (p(-3)=9-3k-18=0), so (-3k=9) and (k=-3). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(-3)=9-3k-18=0), इसलिए (-3k=9) और (k=-3)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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