coefficients se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
71 questions tagged with coefficients.
What is the value of (b) in \(x^2-4\sqrt{2}x+8=0\)?
A. \(-4\sqrt{2}\)
(x) के साथ लगा गुणांक \(-4\sqrt{2}\) है। करणी वाले गुणांक में भी चिन्ह साथ रखें। / The coefficient attached to (x) is \(-4\sqrt{2}\). Keep the sign with radical coefficients too.
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Which equation has (b=0) and (c>0)?
B. \(5x^2+20=0\)
\(5x^2+20=0\) में (x) पद अनुपस्थित है, इसलिए (b=0) और (c=20>0) है। अनुपस्थित पद का गुणांक (0) मानें। / In \(5x^2+20=0\), the (x) term is absent, so (b=0) and (c=20>0). Treat a missing term coefficient as (0).
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What is the value of (ac) in \(3x^2+10x+8=0\)?
A. (24)
यहाँ (a=3) और (c=8), इसलिए (ac=24) है। मध्य पद विभाजन में (ac) उपयोगी होता है। / Here (a=3) and (c=8), so (ac=24). The value (ac) is useful in splitting the middle term.
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If (a=5), (b=-11), (c=-6), which is the corresponding quadratic equation?
B. \(5x^2-11x-6=0\)
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(5x^2-11x-6=0\) मिलता है। ऋण चिन्ह को गुणांक का भाग मानें। / Substituting into \(ax^2+bx+c=0\) gives \(5x^2-11x-6=0\). Treat the negative sign as part of the coefficient.
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For the equation \(-4x^2+6x-9=0\), what is the value of (a-b+c)?
B. (-19)
यहाँ (a=-4), (b=6), (c=-9) हैं। इसलिए (a-b+c=-4-6-9=-19) है। / Here (a=-4), (b=6), (c=-9). Hence (a-b+c=-4-6-9=-19).
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What is the value of (b) in \(x^2+2\sqrt{3}x+3=0\)?
A. \(2\sqrt{3}\)
(x) के साथ लगा गुणांक \(2\sqrt{3}\) है। करणी वाले गुणांक भी सामान्य गुणांक की तरह लिए जाते हैं। / The coefficient attached to (x) is \(2\sqrt{3}\). Radical coefficients are treated like ordinary coefficients.
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Which equation has (b=0) and (c<0)?
B. \(3x^2-12=0\)
\(3x^2-12=0\) में (b=0) और (c=-12) है। अनुपस्थित (x) पद का गुणांक (0) मानें। / In \(3x^2-12=0\), (b=0) and (c=-12). Treat the missing (x) term coefficient as (0).
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What is the value of (ac) in \(2x^2+7x+3=0\)?
A. (6)
यहाँ (a=2) और (c=3), इसलिए (ac=6) है। मध्य पद विधि में (ac) महत्वपूर्ण होता है। / Here (a=2) and (c=3), so (ac=6). The product (ac) is important in the splitting middle term method.
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If a quadratic equation has (a=2), (b=-7), (c=3), which equation is it?
B. \(2x^2-7x+3=0\)
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(2x^2-7x+3=0\) मिलता है। (b) का ऋण चिन्ह साथ रखें। / Substituting in \(ax^2+bx+c=0\) gives \(2x^2-7x+3=0\). Keep the negative sign of (b).
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For the equation \(3x^2-2x+7=0\), what is the value of (a+b+c)?
A. (8)
यहाँ (a=3), (b=-2), (c=7), इसलिए (a+b+c=8) है। गुणांकों के चिन्ह हमेशा साथ लिखें। / Here (a=3), (b=-2), (c=7), so (a+b+c=8). Always include the signs of coefficients.
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If (a=3,\ b=0,\ c=-12), which is the corresponding quadratic equation?
A. \(3x^2-12=0\)
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(3x^2+0x-12=0\) मिलता है। इसे सरल करने पर \(3x^2-12=0\) है। / Substituting in \(ax^2+bx+c=0\) gives \(3x^2+0x-12=0\). Simplifying gives \(3x^2-12=0\).
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Which are the correct values of (a,b,c) in \(-x^2+4x-1=0\)?
A. (a=-1,\ b=4,\ c=-1)
\(x^2\) का गुणांक (-1), (x) का गुणांक (4) और स्थिर पद (-1) है। ऋण चिन्ह को कभी न छोड़ें। / The coefficient of \(x^2\) is (-1), the coefficient of (x) is (4), and the constant term is (-1). Never ignore the negative sign.
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What are the values of (a,b,c) in \(x^2-5x+6=0\)?
A. (a=1,\ b=-5,\ c=6)
मानक रूप से मिलाने पर (a=1,\ b=-5,\ c=6) मिलता है। चिन्हों पर विशेष ध्यान रखें। / Comparing with standard form gives (a=1,\ b=-5,\ c=6). Pay special attention to signs.
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What is the value of (a-b+c) for \(4x^2-2x-6=0\)?
A. (0)
यहां (a=4), (b=-2), (c=-6) हैं। इसलिए (a-b+c=4-(-2)-6=0) है। / Here (a=4), (b=-2), (c=-6). Thus (a-b+c=4-(-2)-6=0).
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What is the value of (a+b+c) for \(5x^2+5x+5=0\)?
C. (15)
यहां (a=5), (b=5), (c=5) हैं। इसलिए (a+b+c=15) है। / Here (a=5), (b=5), (c=5). Therefore (a+b+c=15).
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Which form represents (a=3), (b=-4), (c=-2)?
A. \(3x^2-4x-2=0\)
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(3x^2-4x-2=0\) मिलता है। (b) का चिन्ह ध्यान रखें। / Putting the values in \(ax^2+bx+c=0\) gives \(3x^2-4x-2=0\). Watch the sign of (b).
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What are (a), (b), (c) in \(3x^2-21=0\)?
A. (3,0,-21)
इसे \(3x^2+0x-21=0\) लिखें। इसलिए (a=3), (b=0), (c=-21) हैं। / Write it as \(3x^2+0x-21=0\). So (a=3), (b=0), (c=-21).
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For \(12x^2=0\), what are (a), (b), (c) respectively?
A. (12,0,0)
इसे \(12x^2+0x+0=0\) लिखा जाता है। इसलिए (a=12), (b=0), (c=0) हैं। / It is written as \(12x^2+0x+0=0\). Therefore (a=12), (b=0), (c=0).
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What is the value of (a-b+c) for \(2x^2-3x-5=0\)?
A. (0)
यहां (a=2), (b=-3), (c=-5) हैं। इसलिए (a-b+c=2-(-3)-5=0) है। / Here (a=2), (b=-3), (c=-5). Thus (a-b+c=2-(-3)-5=0).
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What is the value of (a+b+c) for \(4x^2+4x+1=0\)?
C. (9)
यहां (a=4), (b=4), (c=1) हैं। इसलिए (a+b+c=9) है। / Here (a=4), (b=4), (c=1). Therefore (a+b+c=9).
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Which form represents (a=2), (b=-5), (c=3) in \(ax^2+bx+c=0\)?
A. \(2x^2-5x+3=0\)
दिए गए मान सीधे मानक रूप में रखने पर \(2x^2-5x+3=0\) मिलता है। (b) का चिन्ह ध्यान रखें। / Putting the given values in standard form gives \(2x^2-5x+3=0\). Keep the sign of (b) carefully.
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What are (a), (b), (c) in \(7x^2-14=0\)?
A. (7,0,-14)
इसे \(7x^2+0x-14=0\) लिखें। इससे (a=7), (b=0), (c=-14) मिलते हैं। / Write it as \(7x^2+0x-14=0\). Then (a=7), (b=0), (c=-14).
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What is the linear term in \(2x^2+0x-7=0\)?
B. (0x)
रैखिक पद (x) वाला पद होता है। यहां वह (0x) है। / The linear term is the term containing (x). Here it is (0x).
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For \(6x^2=0\), what are (a), (b), (c) respectively?
A. (6,0,0)
इसे \(6x^2+0x+0=0\) लिखा जाता है। इसलिए (a=6), (b=0), (c=0) हैं। / It is written as \(6x^2+0x+0=0\). Therefore (a=6), (b=0), (c=0).
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What is the value of \(x\) in \(9x^2+11=0\)?
C. (0)
इसे \(9x^2+0x+11=0\) लिखा जाता है। इसलिए \(x=0\) है। / It is written as \(9x^2+0x+11=0\). So \(x=0\).
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What is the value of (c) in \(x^2-6x=0\)?
C. (0)
इसे \(x^2-6x+0=0\) लिखा जा सकता है। अतः (c=0) है। / It can be written as \(x^2-6x+0=0\). Hence (c=0).
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What is the value of (b) in \(3x^2+7x-4=0\)?
B. (7)
मानक रूप में (b) (x) का गुणांक होता है। इसलिए (b=7) है। / In standard form, (b) is the coefficient of (x). So (b=7).
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What is the value of (a) in the equation \(5x^2-2x+9=0\)?
A. (5)
मानक रूप \(ax^2+bx+c=0\) में (a) \(x^2\) का गुणांक होता है। यहां (a=5) है। / In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). Here (a=5).
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If (p(x)=2x-2-3x+\sqrt{2}), what type of polynomial is it?
A. वास्तविक गुणांकों वाला द्विघात बहुपदQuadratic polynomial with real coefficients
\(\sqrt{2}\) वास्तविक लेकिन अपरिमेय है, इसलिए गुणांक वास्तविक हैं पर सभी परिमेय नहीं। घात (2) होने से यह द्विघात है। / \(\sqrt{2}\) is real but irrational, so the coefficients are real but not all rational. Since the degree is (2), it is quadratic.
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If (p(x)=x-2-3x-\sqrt{2}), which statement about the coefficients of (p(x)) is correct?
B. एक गुणांक अपरिमेय हैOne coefficient is irrational
स्थिर पद \(-\sqrt{2}\) अपरिमेय है, जबकि बाकी गुणांक परिमेय हैं। शून्यक नियम लागू करने से पहले गुणांकों का प्रकार देखें। / The constant term \(-\sqrt{2}\) is irrational, while the other coefficients are rational. Check coefficient type before applying root rules.
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