यदि (p(x)=x-2 -8x+16) है, तो (p(4+t)) का मान क्या है?
If (p(x)=x-2 -8x+16), what is the value of (p(4+t))?
#substitution
#perfect-square
#polynomial
A \(t^2\)
B \(t^2+4\)
C (4t)
D \(t^2-16\)
Explanation opens after your attempt
Correct Answer
A. \(t^2\)
Step 1
Concept
(p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(t^2\). (p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 3
Exam Tip
(p(x)=(x-4)2 ), इसलिए (p(4+t)=t-2 )। ऐसे प्रश्नों में पहले पूर्ण वर्ग बनाना आसान होता है।
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यदि (p(x)=2x-2 +x-6), तो (2p(1)-p(-2)) का मान क्या है?
If (p(x)=2x-2 +x-6), what is the value of (2p(1)-p(-2))?
#evaluation
#polynomial
#expression
A -(6)
B (0)
C (6)
D -(12)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).
Step 2
Why this answer is correct
The correct answer is A. -(6). (p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).
Step 3
Exam Tip
(p(1)=2+1-6=-3) और (p(-2)=8-2-6=0)। इसलिए (2p(1)-p(-2)=-6)।
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यदि (p(x)=x-2 +ax+a) में (p(1)=0), तो (a) क्या है?
If (p(x)=x-2 +ax+a) and (p(1)=0), what is (a)?
#evaluation
#parameter
#polynomial
A -\(\frac{1}{2}\)
B -(1)
C \(\frac{1}{2}\)
D (1)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{1}{2}\)
Step 1
Concept
(p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{1}{2}\). (p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).
Step 3
Exam Tip
(p(1)=1+a+a=0), इसलिए (2a=-1)। अतः \(a=-\frac{1}{2}\) है।
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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)=x-2 +4x+4), तो (p(-2+h)) का मान क्या है?
If (p(x)=x-2 +4x+4), what is the value of (p(-2+h))?
#substitution
#identity
#polynomial
A \(h^2\)
B (h)
C \(h^2+4\)
D (2h)
Explanation opens after your attempt
Correct Answer
A. \(h^2\)
Step 1
Concept
(p(x)=(x+2)2 ), so (p(-2+h)=h-2 ). Perfect square form makes substitution easier.
Step 2
Why this answer is correct
The correct answer is A. \(h^2\). (p(x)=(x+2)2 ), so (p(-2+h)=h-2 ). Perfect square form makes substitution easier.
Step 3
Exam Tip
(p(x)=(x+2)2 ), इसलिए (p(-2+h)=h-2 )। पूर्ण वर्ग रूप से प्रतिस्थापन आसान हो जाता है।
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यदि (p(x)=x-2 -11x+30) और (q(x)=p(x-2)), तो (q(x)) के शून्यक कौन-से हैं?
If (p(x)=x-2 -11x+30) and (q(x)=p(x-2)), what are the zeroes of (q(x))?
#transformed-zeroes
#polynomial
#expert
A (7,8)
B (3,4)
C (5,6)
D (2,11)
Explanation opens after your attempt
Step 1
Concept
The zeroes of (p(x)) are (5) and (6). For (p(x-2)=0), (x-2=5) or (x-2=6), so the zeroes are (7,8).
Step 2
Why this answer is correct
The correct answer is A. (7,8). The zeroes of (p(x)) are (5) and (6). For (p(x-2)=0), (x-2=5) or (x-2=6), so the zeroes are (7,8).
Step 3
Exam Tip
(p(x)) के शून्यक (5) और (6) हैं। (p(x-2)=0) के लिए (x-2=5) या (x-2=6), इसलिए शून्यक (7,8) हैं।
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यदि (p(x)=(k-3)x-5 +2x-3 -x+9) की घात (3) है, तो (k) क्या है?
If (p(x)=(k-3)x-5 +2x-3 -x+9) has degree (3), what is (k)?
#degree
#parameter
#polynomial
A (3)
B (0)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).
Step 2
Why this answer is correct
The correct answer is A. (3). For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).
Step 3
Exam Tip
घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए। इसलिए (k-3=0) और (k=3)।
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यदि (p(x)=x-3 -2x-2 -13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -2x-2 -13x-10), which of the following is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (5)
B (2)
C -(1)
D -(2)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 2
Why this answer is correct
The correct answer is D. -(2). (p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 3
Exam Tip
(p(-2)=-8-8+26-10=0), इसलिए (-2) शून्यक है। विकल्पों में दिए छोटे मानों को सीधे रखकर जाँचें।
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यदि (p(x)=2x-2 -7x+3), तो (p(x+1)-p(x-1)) क्या होगा?
If (p(x)=2x-2 -7x+3), what will (p(x+1)-p(x-1)) be?
#composition
#substitution
#polynomial
A (8x-14)
B (8x+14)
C (4x-14)
D (4x+14)
Explanation opens after your attempt
Correct Answer
A. (8x-14)
Step 1
Concept
(p(x+1)=2x-2 -3x-2) and (p(x-1)=2x-2 -11x+12), so the difference is (8x-14). Substitute the whole expression in place of (x).
Step 2
Why this answer is correct
The correct answer is A. (8x-14). (p(x+1)=2x-2 -3x-2) and (p(x-1)=2x-2 -11x+12), so the difference is (8x-14). Substitute the whole expression in place of (x).
Step 3
Exam Tip
(p(x+1)=2x-2 -3x-2) और (p(x-1)=2x-2 -11x+12), इसलिए अंतर (8x-14) है। पूरे व्यंजक को (x) की जगह रखें।
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यदि (p(x)=x-2 -8x+15), तो (p(x)-p(3)) क्या है?
If (p(x)=x-2 -8x+15), what is (p(x)-p(3))?
#evaluation
#subtraction
#polynomial
A \(x^2-8x+15\)
B \(x^2-8x+12\)
C \(x^2-8x+9\)
D \(x^2-8x\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+15\)
Step 1
Concept
(p(3)=9-24+15=0), so (p(x)-p(3)=x-2 -8x+15). Find (p(3)) first.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+15\). (p(3)=9-24+15=0), so (p(x)-p(3)=x-2 -8x+15). Find (p(3)) first.
Step 3
Exam Tip
(p(3)=9-24+15=0), इसलिए (p(x)-p(3)=x-2 -8x+15)। पहले (p(3)) निकालें।
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यदि (p(x)=4x-2 -3x+2), तो (p(3x)) क्या है?
If (p(x)=4x-2 -3x+2), what is (p(3x))?
#substitution
#composition
#polynomial
A \(36x^2-9x+2\)
B \(12x^2-9x+2\)
C \(36x^2-3x+2\)
D \(4x^2-9x+2\)
Explanation opens after your attempt
Correct Answer
A. \(36x^2-9x+2\)
Step 1
Concept
(p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2). Square the whole (3x).
Step 2
Why this answer is correct
The correct answer is A. \(36x^2-9x+2\). (p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2). Square the whole (3x).
Step 3
Exam Tip
(p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2)। पूरे (3x) का वर्ग करें।
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यदि (p(x)=x-2 -2x+4), तो (p(x+3)) क्या होगा?
If (p(x)=x-2 -2x+4), what is (p(x+3))?
#composition
#substitution
#polynomial
A \(x^2+4x+7\)
B \(x^2+4x+9\)
C \(x^2+6x+7\)
D \(x^2+6x+9\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+7\)
Step 1
Concept
(p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7). Substitute the whole (x+3) in place of (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+7\). (p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7). Substitute the whole (x+3) in place of (x).
Step 3
Exam Tip
(p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7)। (x) की जगह पूरा (x+3) रखें।
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कौन सा बहुपद (x=0) को शून्य बनाता है लेकिन शून्य बहुपद नहीं है?
Which polynomial makes (x=0) a zero but is not the zero polynomial?
#zero at zero
#constant term
#polynomial
A \(x^2+9\)
B \(4x^3-7x\)
C (5)
D \(x^4+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3-7x\)
Step 1
Concept
Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-7x\). Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 3
Exam Tip
\(4x^3-7x\) में (x=0) रखने पर (0) मिलता है और यह शून्य बहुपद नहीं है। (x=0) के लिए अचर पद (0) होना चाहिए।
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(p(x)=4x-6 -5x-4 +2x-2 -11) में \(x^5\) का गुणांक क्या है?
What is the coefficient of \(x^5\) in (p(x)=4x-6 -5x-4 +2x-2 -11)?
#missing term
#coefficient
#polynomial
A (0)
B (2)
C (4)
D (-5)
Explanation opens after your attempt
Step 1
Concept
The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 3
Exam Tip
\(x^5\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^5\) मानें।
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(\(x^2-9\)\(x^2+9\)) का विस्तृत रूप क्या है?
What is the expanded form of (\(x^2-9\)\(x^2+9\))?
#identity
#expansion
#polynomial
A \(x^4-81\)
B \(x^4+81\)
C \(x^4-18x^2+81\)
D \(x^4+18x^2+81\)
Explanation opens after your attempt
Correct Answer
A. \(x^4-81\)
Step 1
Concept
This is the identity \(a^2-b^2\), so (\(x^2\)2 -92 =x-4 -81). Identities make expansion faster.
Step 2
Why this answer is correct
The correct answer is A. \(x^4-81\). This is the identity \(a^2-b^2\), so (\(x^2\)2 -92 =x-4 -81). Identities make expansion faster.
Step 3
Exam Tip
यह \(a^2-b^2\) की पहचान है, इसलिए (\(x^2\)2 -92 =x-4 -81)। पहचान से विस्तार तेज होता है।
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((2x+5)2 -(2x-1)2 ) का सरल बहुपद रूप क्या है?
What is the simplified polynomial form of ((2x+5)2 -(2x-1)2 )?
#identity
#expansion
#polynomial
A (12x+24)
B (24x+24)
C (24x+12)
D (6x+24)
Explanation opens after your attempt
Correct Answer
B. (24x+24)
Step 1
Concept
By difference of squares, ((6)(4x+4)=24x+24). The identity (a-2 -b-2 =(a-b)(a+b)) is a quick method.
Step 2
Why this answer is correct
The correct answer is B. (24x+24). By difference of squares, ((6)(4x+4)=24x+24). The identity (a-2 -b-2 =(a-b)(a+b)) is a quick method.
Step 3
Exam Tip
अंतर के वर्ग से ((6)(4x+4)=24x+24) मिलता है। पहचान (a-2 -b-2 =(a-b)(a+b)) तेज तरीका है।
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((4x+3)\(x^2-2x+5\)) में अचर पद क्या है?
What is the constant term in ((4x+3)\(x^2-2x+5\))?
#constant term
#multiplication
#polynomial
A (3)
B (5)
C (8)
D (15)
Explanation opens after your attempt
Step 1
Concept
The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
Step 2
Why this answer is correct
The correct answer is D. (15). The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
Step 3
Exam Tip
अचर पद केवल \(3\cdot5=15\) से आता है। अचर पद के लिए अचर भागों का गुणन देखें।
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(p(x)=6x-6 -5x-5 +4x-3 -2x-2 +x-7) में विषम घात वाले पदों के गुणांकों का योग क्या है?
What is the sum of coefficients of odd-power terms in (p(x)=6x-6 -5x-5 +4x-3 -2x-2 +x-7)?
#coefficients
#odd powers
#polynomial
A (-2)
B (0)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (-5), (4), and (1). Their sum is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). The coefficients of odd powers \(x^5\), \(x^3\), and (x) are (-5), (4), and (1). Their sum is (0).
Step 3
Exam Tip
विषम घातों \(x^5\), \(x^3\) और (x) के गुणांक (-5), (4) और (1) हैं। उनका योग (0) है।
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यदि (p(x)=4x-4 +kx-3 -6x+1) में सभी गुणांकों का योग (5) है, तो (k) क्या है?
If the sum of all coefficients of (p(x)=4x-4 +kx-3 -6x+1) is (5), what is (k)?
#sum of coefficients
#parameter
#polynomial
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The sum of coefficients is (4+k+0-6+1=k-1), so (k-1=5) and (k=6). The sum of coefficients is found by (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (6). The sum of coefficients is (4+k+0-6+1=k-1), so (k-1=5) and (k=6). The sum of coefficients is found by (p(1)).
Step 3
Exam Tip
गुणांकों का योग (4+k+0-6+1=k-1) है, इसलिए (k-1=5) और (k=6)। गुणांकों का योग (p(1)) से मिलता है।
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(p(x)=8x-4 -3x-3 -4x+2) में सभी गुणांकों का योग क्या है?
What is the sum of all coefficients in (p(x)=8x-4 -3x-3 -4x+2)?
#sum of coefficients
#evaluation
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of all coefficients is (8-3+0-4+2=3). It is also equal to (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (3). The sum of all coefficients is (8-3+0-4+2=3). It is also equal to (p(1)).
Step 3
Exam Tip
सभी गुणांकों का योग (8-3+0-4+2=3) है। यह (p(1)) के बराबर भी होता है।
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यदि अशून्य बहुपद (p(x)) की घात (6) और (q(x)) की घात (3) है, तो (p(x)q(x)) की घात क्या होगी?
If non-zero polynomial (p(x)) has degree (6) and (q(x)) has degree (3), what will be the degree of (p(x)q(x))?
#degree
#product
#polynomial
A (3)
B (6)
C (9)
D (18)
Explanation opens after your attempt
Step 1
Concept
In the product of two non-zero polynomials, degrees add, so (6+3=9). In multiplication, look at the highest-power terms.
Step 2
Why this answer is correct
The correct answer is C. (9). In the product of two non-zero polynomials, degrees add, so (6+3=9). In multiplication, look at the highest-power terms.
Step 3
Exam Tip
दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (6+3=9)। गुणन में उच्चतम घातों का गुणन देखें।
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यदि (p(x)=(a-1)x-6 +(a+2)x-4 -5x+7) की घात (4) है, तो (a) क्या होगा?
If the degree of (p(x)=(a-1)x-6 +(a+2)x-4 -5x+7) is (4), what will (a) be?
#degree
#parameter
#polynomial
A (-2)
B (1)
C (2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (4), the coefficient of \(x^6\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (a=1).
Step 2
Why this answer is correct
The correct answer is B. (1). For degree (4), the coefficient of \(x^6\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (a=1).
Step 3
Exam Tip
घात (4) के लिए \(x^6\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (a=1) पर दोनों शर्तें पूरी होती हैं।
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यदि (p(x)=2x-2 -5x+3), तो (p(x+2)-p(x)) क्या होगा?
If (p(x)=2x-2 -5x+3), what will (p(x+2)-p(x)) be?
#composition
#substitution
#polynomial
A (8x-2)
B (8x+2)
C (4x-2)
D (4x+2)
Explanation opens after your attempt
Step 1
Concept
(p(x+2)=2(x+2)2 -5(x+2)+3=2x-2 +3x+1), so the difference is (8x+2). Substitute the whole (x+2) correctly.
Step 2
Why this answer is correct
The correct answer is B. (8x+2). (p(x+2)=2(x+2)2 -5(x+2)+3=2x-2 +3x+1), so the difference is (8x+2). Substitute the whole (x+2) correctly.
Step 3
Exam Tip
(p(x+2)=2(x+2)2 -5(x+2)+3=2x-2 +3x+1), इसलिए अंतर (8x+2) है। पूरे (x+2) को सही जगह रखें।
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यदि (x=0), (p(x)=7x-3 -2x) का शून्यक है, तो कारण क्या है?
If (x=0) is a zero of (p(x)=7x-3 -2x), what is the reason?
#zero-at-origin
#factor
#polynomial
A हर पद में (x) गुणनखंड है / Every term has factor (x)
B स्थिर पद (7) है / Constant term is (7)
C घात (3) है / Degree is (3)
D गुणांक ऋणात्मक है / A coefficient is negative
Explanation opens after your attempt
Correct Answer
A. हर पद में (x) गुणनखंड है / Every term has factor (x)
Step 1
Concept
(p(x)=x\(7x^2-2\)), so at (x=0) the value is (0). If every term has (x), then (0) is a zero.
Step 2
Why this answer is correct
The correct answer is A. हर पद में (x) गुणनखंड है / Every term has factor (x). (p(x)=x\(7x^2-2\)), so at (x=0) the value is (0). If every term has (x), then (0) is a zero.
Step 3
Exam Tip
(p(x)=x\(7x^2-2\)), इसलिए (x=0) पर मान (0) होता है। यदि हर पद में (x) हो, तो (0) शून्यक होता है।
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यदि (p(x)=ax+b) और \(a\neq0\), तो इसका शून्यक क्या है?
If (p(x)=ax+b) and \(a\neq0\), what is its zero?
#linear-zero
#general-form
#polynomial
A -\(\frac{b}{a}\)
B \(\frac{b}{a}\)
C -\(\frac{a}{b}\)
D \(\frac{a}{b}\)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{b}{a}\)
Step 1
Concept
Putting (ax+b=0) gives \(x=-\frac{b}{a}\). A linear polynomial has exactly one zero.
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{b}{a}\). Putting (ax+b=0) gives \(x=-\frac{b}{a}\). A linear polynomial has exactly one zero.
Step 3
Exam Tip
(ax+b=0) रखने पर \(x=-\frac{b}{a}\) मिलता है। रेखीय बहुपद में केवल एक शून्यक होता है।
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यदि (p(x)=x-3 -2x-2 -5x+6), तो (p(3)) का मान क्या है?
If (p(x)=x-3 -2x-2 -5x+6), what is the value of (p(3))?
#evaluation
#zero
#polynomial
A (0)
B (6)
C (-6)
D (12)
Explanation opens after your attempt
Step 1
Concept
(p(3)=27-18-15+6=0). Therefore (3) is also a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(3)=27-18-15+6=0). Therefore (3) is also a zero of this polynomial.
Step 3
Exam Tip
(p(3)=27-18-15+6=0) है। इसलिए (3) भी इस बहुपद का शून्यक है।
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यदि (p(x)=2x-3 +3x-2 -8x+3), तो (x-1) से भाग देने पर शेष क्या है?
If (p(x)=2x-3 +3x-2 -8x+3), what is the remainder when divided by (x-1)?
#remainder-theorem
#division
#polynomial
A (0)
B (2)
C (3)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The remainder is (p(1)=2+3-8+3=0). On division by (x-a), the remainder is (p(a)).
Step 2
Why this answer is correct
The correct answer is A. (0). The remainder is (p(1)=2+3-8+3=0). On division by (x-a), the remainder is (p(a)).
Step 3
Exam Tip
शेष (p(1)=2+3-8+3=0) है। (x-a) से भाग में शेष (p(a)) होता है।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को (x=-2), (x=0) और (x=3) पर काटता है, तो सबसे कम घात का मोनिक बहुपद कौन-सा है?
If the graph of a polynomial cuts the (x)-axis at (x=-2), (x=0), and (x=3), which is the monic polynomial of least degree?
#graph-zeroes
#least-degree
#polynomial
A \(x^3-x^2-6x\)
B \(x^3+x^2-6x\)
C \(x^3-6x\)
D \(x^3+6x^2-x\)
Explanation opens after your attempt
Correct Answer
A. \(x^3-x^2-6x\)
Step 1
Concept
The zeroes are (-2,0,3), so the polynomial is (x(x+2)(x-3)=x-3 -x-2 -6x). Intersections with the (x)-axis give zeroes.
Step 2
Why this answer is correct
The correct answer is A. \(x^3-x^2-6x\). The zeroes are (-2,0,3), so the polynomial is (x(x+2)(x-3)=x-3 -x-2 -6x). Intersections with the (x)-axis give zeroes.
Step 3
Exam Tip
शून्यक (-2,0,3) हैं, इसलिए बहुपद (x(x+2)(x-3)=x-3 -x-2 -6x) है। (x)-अक्ष काटने के बिंदु शून्यक बताते हैं।
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यदि (p(x)=x-3 +3x-2 -4x-12), तो निम्न में से कौन-सा गुणनखंड है?
If (p(x)=x-3 +3x-2 -4x-12), which of the following is a factor?
#factor-theorem
#cubic
#polynomial
A (x+3)
B (x-3)
C (x+2)
D (x-4)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=-27+27+12-12=0), so (x+3) is a factor. For (x+a), test (x=-a).
Step 2
Why this answer is correct
The correct answer is A. (x+3). (p(-3)=-27+27+12-12=0), so (x+3) is a factor. For (x+a), test (x=-a).
Step 3
Exam Tip
(p(-3)=-27+27+12-12=0), इसलिए (x+3) गुणनखंड है। (x+a) के लिए (x=-a) रखकर जाँचें।
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यदि (p(x)=x-3 -4x-2 +x+6), तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -4x-2 +x+6), which of these is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (2)
B (1)
C (-1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 3
Exam Tip
(p(2)=8-16+2+6=0), इसलिए (2) शून्यक है। विकल्पों में छोटे पूर्णांकों को पहले जाँचें।
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