यदि (p(x)=x-2 +kx+16) का एक शून्यक दूसरे का दुगुना है और दोनों धनात्मक हैं, तो (k) क्या होगा?
If one zero of (p(x)=x-2 +kx+16) is twice the other and both are positive, what is (k)?
#zeroes-ratio
#parameter
#expert
A -\(6\sqrt{2}\)
B \(6\sqrt{2}\)
C -(8)
D (8)
Explanation opens after your attempt
Correct Answer
A. -\(6\sqrt{2}\)
Step 1
Concept
Let the zeroes be (t) and (2t), then \(2t^2=16\) gives \(t=2\sqrt{2}\). The sum is \(6\sqrt{2}\), so \(-k=6\sqrt{2}\) and \(k=-6\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. -\(6\sqrt{2}\). Let the zeroes be (t) and (2t), then \(2t^2=16\) gives \(t=2\sqrt{2}\). The sum is \(6\sqrt{2}\), so \(-k=6\sqrt{2}\) and \(k=-6\sqrt{2}\).
Step 3
Exam Tip
शून्यक (t) और (2t) मानें, तो \(2t^2=16\) से \(t=2\sqrt{2}\) है। योग \(6\sqrt{2}\) है, इसलिए \(-k=6\sqrt{2}\) और \(k=-6\sqrt{2}\)।
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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 (p(x)=kx-2 -6x+4) के शून्यकों का गुणनफल (2) है, तो (k) क्या है?
If the product of zeroes of (p(x)=kx-2 -6x+4) is (2), what is (k)?
#product-zeroes
#parameter
#quadratic
A (2)
B (4)
C (1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{4}{k}\), so \(\frac{4}{k}=2\) and (k=2). Product equals constant term divided by leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). The product is \(\frac{4}{k}\), so \(\frac{4}{k}=2\) and (k=2). Product equals constant term divided by leading coefficient.
Step 3
Exam Tip
गुणनफल \(\frac{4}{k}\) है, इसलिए \(\frac{4}{k}=2\) और (k=2)। गुणनफल में स्थिर पद को प्रमुख गुणांक से भाग देते हैं।
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यदि (p(x)=3x-2 +(m-1 )x-2) के शून्यकों का योग (0) है, तो (m) क्या है?
If the sum of zeroes of (p(x)=3x-2 +(m-1 )x-2) is (0), what is (m)?
#sum-zeroes
#parameter
#coefficient
A (1)
B (0)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The sum is \(-\frac{m-1}{3}\); setting it to (0) gives (m-1 =0). When the sum is zero, the coefficient of (x) becomes zero.
Step 2
Why this answer is correct
The correct answer is A. (1). The sum is \(-\frac{m-1}{3}\); setting it to (0) gives (m-1 =0). When the sum is zero, the coefficient of (x) becomes zero.
Step 3
Exam Tip
योग \(-\frac{m-1}{3}\) है, इसे (0) रखने पर (m-1 =0) मिलता है। शून्य योग में (x) का गुणांक (0) हो जाता है।
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यदि (p(x)=x-2 -2(k+1)x+k-2 ) के शून्यकों का योग (10) है, तो (k) क्या है?
If the sum of zeroes of (p(x)=x-2 -2(k+1)x+k-2 ) is (10), what is (k)?
#parameter
#sum-zeroes
#quadratic
A (4)
B (5)
C (9)
D (3)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (2(k+1)), so (2(k+1)=10) and (k=4). Handle the negative sign carefully in the formula.
Step 2
Why this answer is correct
The correct answer is A. (4). The sum of zeroes is (2(k+1)), so (2(k+1)=10) and (k=4). Handle the negative sign carefully in the formula.
Step 3
Exam Tip
शून्यकों का योग (2(k+1)) है, इसलिए (2(k+1)=10) और (k=4)। सूत्र लगाते समय ऋण चिह्न संभालें।
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किस मान के लिए (p(x)=(m-2 )x-4 +3x-2 +x+1) की घात (2) से अधिक नहीं होगी?
For which value will (p(x)=(m-2 )x-4 +3x-2 +x+1) have degree not more than (2)?
#degree
#parameter
#polynomial
A (m=2)
B (m=0)
C (m=1)
D (m=-2)
Explanation opens after your attempt
Step 1
Concept
To make the degree not more than (2), the coefficient of \(x^4\) must be (0), so (m-2 =0). Degree reduces only when the highest term vanishes.
Step 2
Why this answer is correct
The correct answer is A. (m=2). To make the degree not more than (2), the coefficient of \(x^4\) must be (0), so (m-2 =0). Degree reduces only when the highest term vanishes.
Step 3
Exam Tip
घात (2) से अधिक न हो इसके लिए \(x^4\) का गुणांक (0) चाहिए, अतः (m-2 =0)। उच्चतम पद हटाकर ही घात घटती है।
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यदि (p(x)=x-2 +px+q), (p(0)=-8) और (p(4)=0), तो (p) का मान क्या है?
If (p(x)=x-2 +px+q), (p(0)=-8), and (p(4)=0), what is the value of (p)?
#parameter
#quadratic
#evaluation
A (-2)
B (-1)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(0)=q=-8) and (p(4)=16+4p-8=0), so (4p=-8) and (p=-2). Find the constant term first.
Step 2
Why this answer is correct
The correct answer is A. (-2). (p(0)=q=-8) and (p(4)=16+4p-8=0), so (4p=-8) and (p=-2). Find the constant term first.
Step 3
Exam Tip
(p(0)=q=-8) और (p(4)=16+4p-8=0), इसलिए (4p=-8) और (p=-2)। पहले अचर पद निकालें।
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यदि (p(x)=x-2 +kx+16) पूर्ण वर्ग बहुपद है और (k<0), तो (k) क्या है?
If (p(x)=x-2 +kx+16) is a perfect square polynomial and (k<0), what is (k)?
#perfect square
#parameter
#quadratic
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
For (x-2 +kx+16=(x-4)2 ), (k=-8). In a perfect square, the middle term is (2ab).
Step 2
Why this answer is correct
The correct answer is A. (-8). For (x-2 +kx+16=(x-4)2 ), (k=-8). In a perfect square, the middle term is (2ab).
Step 3
Exam Tip
(x-2 +kx+16=(x-4)2 ) होने पर (k=-8)। पूर्ण वर्ग में मध्य पद (2ab) होता है।
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यदि (p(x)=mx-4 +(m+2)x-3 +5x+1) की घात (3) है, तो (m) क्या है?
If the degree of (p(x)=mx-4 +(m+2)x-3 +5x+1) is (3), what is (m)?
#degree
#parameter
#conditions
A (-2)
B (0)
C (2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (3), the coefficient of \(x^4\) must be (0) and the coefficient of \(x^3\) must be non-zero. For (m=0), (m+2=2).
Step 2
Why this answer is correct
The correct answer is B. (0). For degree (3), the coefficient of \(x^4\) must be (0) and the coefficient of \(x^3\) must be non-zero. For (m=0), (m+2=2).
Step 3
Exam Tip
घात (3) के लिए \(x^4\) का गुणांक (0) चाहिए और \(x^3\) का गुणांक अशून्य चाहिए। (m=0) पर (m+2=2) है।
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यदि (p(x)=x-3 +ax-2 +bx-6) में (x=1) और (x=2) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=2) are both zeros of (p(x)=x-3 +ax-2 +bx-6), what is (a)?
#zeros
#cubic
#parameter
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=0) gives (a+b=5) and (p(2)=0) gives (2a+b=-1), so (a=-6). None of the listed choices is correct.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=0) gives (a+b=5) and (p(2)=0) gives (2a+b=-1), so (a=-6). None of the listed choices is correct.
Step 3
Exam Tip
(p(1)=0) से (a+b=5) और (p(2)=0) से (2a+b=-1), इसलिए (a=-6) नहीं बल्कि (a=-6) आता है। विकल्पों में कोई सही नहीं है।
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यदि (p(x)=x-3 +ax-2 +bx+12) में (x=1) और (x=-3) दोनों शून्य हैं, तो (a+b) क्या है?
If (x=1) and (x=-3) are both zeros of (p(x)=x-3 +ax-2 +bx+12), what is (a+b)?
#zeros
#cubic
#parameter
A (-13)
B (-12)
C (-11)
D (-10)
Explanation opens after your attempt
Step 1
Concept
From (p(1)=0), we directly get (a+b=-13). The second condition checks consistency, but the first is enough for the asked sum.
Step 2
Why this answer is correct
The correct answer is A. (-13). From (p(1)=0), we directly get (a+b=-13). The second condition checks consistency, but the first is enough for the asked sum.
Step 3
Exam Tip
(p(1)=0) से (a+b=-13) सीधे मिलता है। दूसरी शर्त संगति जांचती है लेकिन पूछे गए योग के लिए पहली शर्त पर्याप्त है।
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यदि (p(x)=3x-2 +bx+c), (p(0)=7) और (p(1)=2), तो (b) क्या है?
If (p(x)=3x-2 +bx+c), (p(0)=7), and (p(1)=2), what is (b)?
#parameter
#constant term
#evaluation
A (-8)
B (-7)
C (-6)
D (-5)
Explanation opens after your attempt
Step 1
Concept
(p(0)=c=7) and (p(1)=3+b+7=2), so (b=-8). (x=0) gives the constant term directly.
Step 2
Why this answer is correct
The correct answer is A. (-8). (p(0)=c=7) and (p(1)=3+b+7=2), so (b=-8). (x=0) gives the constant term directly.
Step 3
Exam Tip
(p(0)=c=7) और (p(1)=3+b+7=2), इसलिए (b=-8)। (x=0) अचर पद तुरंत देता है।
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किस मान के लिए ((n-2)x-2 +(n+1)x+5) अचर बहुपद बन सकता है?
For what value of (n) can ((n-2)x-2 +(n+1)x+5) become a constant polynomial?
#constant polynomial
#parameter
#condition
A (n=2)
B (n=-1)
C (n=1)
D ऐसा कोई मान नहीं / No such value
Explanation opens after your attempt
Correct Answer
D. ऐसा कोई मान नहीं / No such value
Step 1
Concept
For a constant polynomial, both (n-2=0) and (n+1=0) are needed, which is impossible together. All variable terms must vanish.
Step 2
Why this answer is correct
The correct answer is D. ऐसा कोई मान नहीं / No such value. For a constant polynomial, both (n-2=0) and (n+1=0) are needed, which is impossible together. All variable terms must vanish.
Step 3
Exam Tip
अचर बहुपद के लिए (n-2=0) और (n+1=0) दोनों चाहिए, जो साथ संभव नहीं हैं। सभी चर वाले पद हटने चाहिए।
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यदि (p(x)=2x-3 +rx-2 +s), (p(0)=-3) और (p(1)=4), तो (r) क्या है?
If (p(x)=2x-3 +rx-2 +s), (p(0)=-3), and (p(1)=4), what is (r)?
#parameter
#evaluation
#cubic
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(0)=s=-3) and (p(1)=2+r-3=4), so (r=5). First use (x=0) to find the constant term.
Step 2
Why this answer is correct
The correct answer is C. (5). (p(0)=s=-3) and (p(1)=2+r-3=4), so (r=5). First use (x=0) to find the constant term.
Step 3
Exam Tip
(p(0)=s=-3) और (p(1)=2+r-3=4), इसलिए (r=5)। पहले (x=0) से अचर पद निकालें।
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यदि (p(x)=x-3 +ax+b), (p(1)=6) और (p(-1)=-4), तो (a) का मान क्या है?
If (p(x)=x-3 +ax+b), (p(1)=6), and (p(-1)=-4), what is the value of (a)?
#parameter
#cubic
#evaluation
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).
Step 2
Why this answer is correct
The correct answer is C. (4). The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).
Step 3
Exam Tip
शर्तों से (1+a+b=6) और (-1-a+b=-4) मिलते हैं। इन्हें हल करने पर (a=4) मिलता है।
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यदि बहुपद (p(x)=3x-3 +kx-2 -7x+2) में सभी गुणांकों का योग (5) है, तो (k) क्या है?
If the sum of all coefficients of (p(x)=3x-3 +kx-2 -7x+2) is (5), what is (k)?
#sum of coefficients
#parameter
#polynomial
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The sum of coefficients is (3+k-7+2=k-2), so (k-2=5) and (k=7). The sum of coefficients is (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (7). The sum of coefficients is (3+k-7+2=k-2), so (k-2=5) and (k=7). The sum of coefficients is (p(1)).
Step 3
Exam Tip
गुणांकों का योग (3+k-7+2=k-2) है, इसलिए (k-2=5) और (k=7)। गुणांकों का योग (p(1)) होता है।
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यदि (p(x)=x-2 +ax+b), (p(2)=0) और (p(4)=0), तो (a+b) क्या है?
If (p(x)=x-2 +ax+b), (p(2)=0), and (p(4)=0), what is (a+b)?
#zeros
#quadratic
#parameter
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The zeros are (2) and (4), so the polynomial is ((x-2)(x-4)=x-2 -6x+8). Hence (a+b=-6+8=2).
Step 2
Why this answer is correct
The correct answer is C. (2). The zeros are (2) and (4), so the polynomial is ((x-2)(x-4)=x-2 -6x+8). Hence (a+b=-6+8=2).
Step 3
Exam Tip
शून्य (2) और (4) हैं, इसलिए बहुपद ((x-2)(x-4)=x-2 -6x+8) है। अतः (a+b=-6+8=2)।
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किस मान के लिए (p(x)=x-3 -5x-2 +mx+8) में (p(1)=0) होगा?
For what value of (m) will (p(1)=0) in (p(x)=x-3 -5x-2 +mx+8)?
#parameter
#evaluation
#cubic
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.
Step 3
Exam Tip
(p(1)=1-5+m+8=m+4), इसलिए (m=-4)। दिए गए मान को रखकर समीकरण हल करें।
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यदि (x=-2), बहुपद (p(x)=x-2 +kx-8) का शून्य है, तो (k) क्या है?
If (x=-2) is a zero of (p(x)=x-2 +kx-8), what is (k)?
#zero
#parameter
#quadratic
A (-4)
B (-2)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=4-2k-8=0), so (-2k=4) and (k=-2). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (-2). (p(-2)=4-2k-8=0), so (-2k=4) and (k=-2). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(-2)=4-2k-8=0), इसलिए (-2k=4) और (k=-2)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (p(x)=kx-3 -2x-2 +5x-4) और (p(1)=7), तो (k) का मान क्या है?
If (p(x)=kx-3 -2x-2 +5x-4) and (p(1)=7), what is the value of (k)?
#evaluation
#parameter
#cubic polynomial
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(p(1)=k-2+5-4=k-1), so (k-1=7) and (k=8). Substitute first and then form a simple equation.
Step 2
Why this answer is correct
The correct answer is C. (8). (p(1)=k-2+5-4=k-1), so (k-1=7) and (k=8). Substitute first and then form a simple equation.
Step 3
Exam Tip
(p(1)=k-2+5-4=k-1), इसलिए (k-1=7) और (k=8)। मान रखने के बाद सरल समीकरण बनाएं।
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यदि (p(x)=(m+2)x-5 +(m-3 )x-4 +6x-1) की घात (4) है, तो (m) क्या होगा?
If the degree of (p(x)=(m+2)x-5 +(m-3 )x-4 +6x-1) is (4), what is (m)?
#degree
#parameter
#polynomial
A (-2)
B (2)
C (3)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (m=-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (m=-2).
Step 3
Exam Tip
घात (4) के लिए \(x^5\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (m=-2) पर दोनों शर्तें पूरी होती हैं।
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यदि (p(x)=x-2 +ax+b), (p(2)=3) और (p(-1)=6), तो (a+b) का मान क्या है?
If (p(x)=x-2 +ax+b), (p(2)=3), and (p(-1)=6), what is the value of (a+b)?
#parameter
#quadratic
#evaluation
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
The conditions give (2a+b=-1) and (-a+b=5), so (a=-2), (b=3), and (a+b=1). When two values are given, form two equations.
Step 2
Why this answer is correct
The correct answer is C. (1). The conditions give (2a+b=-1) and (-a+b=5), so (a=-2), (b=3), and (a+b=1). When two values are given, form two equations.
Step 3
Exam Tip
शर्तों से (2a+b=-1) और (-a+b=5) मिलते हैं, इसलिए (a=-2), (b=3) और (a+b=1)। दो मान दिए हों तो दो समीकरण बनाएं।
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द्विघात बहुपद \(kx^2+6x+4\) के शून्यकों का योग (-3) है। (k) का मान क्या है?
The sum of zeroes of the quadratic polynomial \(kx^2+6x+4\) is (-3). What is (k)?
#polynomials
#parameter
#sum_zeroes
#hard
A (2)
B (-2)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The sum is \(-\frac{6}{k}\), and it equals (-3). Therefore, (k=2).
Step 2
Why this answer is correct
The correct answer is A. (2). The sum is \(-\frac{6}{k}\), and it equals (-3). Therefore, (k=2).
Step 3
Exam Tip
योग \(-\frac{6}{k}\) है और यह (-3) है। इसलिए (k=2) होगा।
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यदि (p(x)=x-2 -4x+k) और (p(1)=p(3)), तो (k) के बारे में क्या कहा जा सकता है?
If (p(x)=x-2 -4x+k) and (p(1)=p(3)), what can be said about (k)?
#polynomials
#evaluation
#parameter
#hard
A (k=1)
B (k=3)
C कोई भी वास्तविक मान / Any real value
D कोई मान संभव नहीं / No value possible
Explanation opens after your attempt
Correct Answer
C. कोई भी वास्तविक मान / Any real value
Step 1
Concept
(p(1)=k-3) and (p(3)=k-3), so they are equal. Hence (k) can be any real value.
Step 2
Why this answer is correct
The correct answer is C. कोई भी वास्तविक मान / Any real value. (p(1)=k-3) and (p(3)=k-3), so they are equal. Hence (k) can be any real value.
Step 3
Exam Tip
(p(1)=k-3) और (p(3)=k-3) दोनों बराबर हैं। इसलिए (k) कोई भी वास्तविक मान हो सकता है।
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यदि (x+1) बहुपद \(2x^3+kx^2-5x+2\) का गुणनखंड है, तो (k) का सही मान क्या है?
If (x+1) is a factor of \(2x^3+kx^2-5x+2\), what is the correct value of (k)?
#polynomials
#factor_theorem
#parameter
#hard
A (-5)
B (5)
C (-1)
D (1)
Explanation opens after your attempt
Step 1
Concept
Putting (p(-1)=0) gives (-2+k+5+2=0). Therefore, (k=-5) is correct.
Step 2
Why this answer is correct
The correct answer is A. (-5). Putting (p(-1)=0) gives (-2+k+5+2=0). Therefore, (k=-5) is correct.
Step 3
Exam Tip
(p(-1)=0) रखने पर (-2+k+5+2=0) मिलता है। इसलिए (k=-5) सही है।
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यदि (x+1) बहुपद \(2x^3+kx^2-5x+2\) का गुणनखंड है, तो (k) का मान क्या है?
If (x+1) is a factor of \(2x^3+kx^2-5x+2\), what is (k)?
#polynomials
#factor_theorem
#parameter
#hard
A (5)
B (-5)
C (1)
D (-1)
Explanation opens after your attempt
Step 1
Concept
If (x+1) is a factor, then (p(-1)=0). From (-2+k+5+2=0), we get (k=-5).
Step 2
Why this answer is correct
The correct answer is A. (5). If (x+1) is a factor, then (p(-1)=0). From (-2+k+5+2=0), we get (k=-5).
Step 3
Exam Tip
(x+1) गुणनखंड होने पर (p(-1)=0) होगा। (-2+k+5+2=0) से (k=-5) नहीं बल्कि (k=-5) मिलता है।
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यदि (p(x)=x-2 +px+q) और (p(0)=6), (p(2)=0), तो (p) का मान क्या है?
If (p(x)=x-2 +px+q) and (p(0)=6), (p(2)=0), what is the value of (p)?
#parameter
#quadratic
#evaluation
A (-5)
B (-4)
C (-3)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(0)=q=6) and (p(2)=4+2p+6=0), so (p=-5). Find the constant term first.
Step 2
Why this answer is correct
The correct answer is A. (-5). (p(0)=q=6) and (p(2)=4+2p+6=0), so (p=-5). Find the constant term first.
Step 3
Exam Tip
(p(0)=q=6) और (p(2)=4+2p+6=0), इसलिए (p=-5)। पहले अचर पद निकालें।
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यदि (p(x)=x-2 +kx+9) पूर्ण वर्ग बहुपद है और (k>0), तो (k) क्या है?
If (p(x)=x-2 +kx+9) is a perfect square polynomial and (k>0), what is (k)?
#perfect square
#parameter
#quadratic
A (3)
B (6)
C (9)
D (18)
Explanation opens after your attempt
Step 1
Concept
For (x-2 +kx+9=(x+3)2 ), (k=6). In a perfect square, the middle term is (2ab).
Step 2
Why this answer is correct
The correct answer is B. (6). For (x-2 +kx+9=(x+3)2 ), (k=6). In a perfect square, the middle term is (2ab).
Step 3
Exam Tip
(x-2 +kx+9=(x+3)2 ) होने पर (k=6)। पूर्ण वर्ग में मध्य पद (2ab) होता है।
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यदि (p(x)=mx-3 +(m-1 )x-2 +2x+1) की घात (2) है, तो (m) क्या है?
If the degree of (p(x)=mx-3 +(m-1 )x-2 +2x+1) is (2), what is (m)?
#degree
#parameter
#conditions
A (0)
B (1)
C (2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).
Step 2
Why this answer is correct
The correct answer is A. (0). For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).
Step 3
Exam Tip
घात (2) के लिए \(x^3\) का गुणांक (0) चाहिए और \(x^2\) का गुणांक अशून्य चाहिए। (m=0) पर ये दोनों शर्तें पूरी होती हैं।
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यदि (p(x)=x-3 +ax-2 +bx+4) में (x=1) और (x=-1) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=-1) are both zeros of (p(x)=x-3 +ax-2 +bx+4), what is (a)?
#zeros
#cubic
#parameter
A (-4)
B (-2)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.
Step 3
Exam Tip
(p(1)=1+a+b+4=0) और (p(-1)=-1+a-b+4=0), इसलिए (2a+4=0) नहीं बल्कि जोड़ने पर (2a+8=0), अतः (a=-4)। संकेतों को सावधानी से जोड़ें।
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