zero se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
111 questions tagged with zero.
For (p(x)=x-2-1), what is (p(-1))?
A. (0)
(p(-1)=(-1)2-1=1-1=0). Use brackets when substituting a negative value.
The correct answer is A. (0). (p(-1)=(-1)2-1=1-1=0). Use brackets when substituting a negative value.
(p(-1)=(-1)2-1=1-1=0) है। कोष्ठक लगाकर ऋणात्मक मान रखें।
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What conclusion follows when (x=2) is substituted in (p(x)=4x-8)?
A. (2) शून्यक है(2) is a zero
(p(2)=4\cdot2-8=0), so (2) is a zero. To test a zero, the value must be (0).
The correct answer is A. (2) शून्यक है / (2) is a zero. (p(2)=4\cdot2-8=0), so (2) is a zero. To test a zero, the value must be (0).
(p(2)=4\cdot2-8=0), इसलिए (2) शून्यक है। शून्यक जांचने के लिए मान (0) आना चाहिए।
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What is the value of \(x^3-1\) when (x=1)?
A. (0)
\(1^3-1=0\). So (1) is also a zero of this polynomial.
The correct answer is A. (0). \(1^3-1=0\). So (1) is also a zero of this polynomial.
\(1^3-1=0\) है। इसलिए (1) इस बहुपद का शून्यक भी है।
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Which value is a zero of the polynomial \(x^2-9\)?
B. (3)
\(3^2-9=0\), so (3) is a zero. Substituting options is an easy method.
The correct answer is B. (3). \(3^2-9=0\), so (3) is a zero. Substituting options is an easy method.
\(3^2-9=0\), इसलिए (3) शून्यक है। विकल्पों को रखकर जांचना आसान तरीका है।
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Which is the zero of (p(x)=5x+10)?
B. (-2)
From (5x+10=0), we get (x=-2). Do not forget the sign change.
The correct answer is B. (-2). From (5x+10=0), we get (x=-2). Do not forget the sign change.
(5x+10=0) से (x=-2) मिलता है। चिह्न बदलना न भूलें।
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If (p(x)=3x-12), what is its zero?
B. (4)
From (3x-12=0), we get (x=4). For a linear polynomial, form a simple equation.
The correct answer is B. (4). From (3x-12=0), we get (x=4). For a linear polynomial, form a simple equation.
(3x-12=0) से (x=4) मिलता है। रैखिक बहुपद में सीधे समीकरण बनाएं।
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Which value is a zero of (p(x)=x+4)?
B. (-4)
(p(-4)=-4+4=0), so (-4) is the zero. For (x+a), the zero is (-a).
The correct answer is B. (-4). (p(-4)=-4+4=0), so (-4) is the zero. For (x+a), the zero is (-a).
(p(-4)=-4+4=0), इसलिए (-4) शून्यक है। रैखिक बहुपद (x+a) का शून्यक (-a) होता है।
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If (p(x)=x-6), what is (p(6))?
A. (0)
(p(6)=6-6=0), so (6) is a zero of the polynomial. At a zero, the polynomial value is (0).
The correct answer is A. (0). (p(6)=6-6=0), so (6) is a zero of the polynomial. At a zero, the polynomial value is (0).
(p(6)=6-6=0), इसलिए (6) इस बहुपद का शून्यक है। शून्यक पर बहुपद का मान (0) आता है।
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If (p(x)=x-2-4), what is (p(2))?
A. (0)
(p(2)=22-4=0). So (2) is a zero of this polynomial.
The correct answer is A. (0). (p(2)=22-4=0). So (2) is a zero of this polynomial.
(p(2)=22-4=0) है। इसलिए (2) इस बहुपद का शून्यक है।
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If (p(x)=x-2-1), what is (p(1))?
A. (0)
(p(1)=12-1=0). When (p(a)=0), (a) is called a zero.
The correct answer is A. (0). (p(1)=12-1=0). When (p(a)=0), (a) is called a zero.
(p(1)=12-1=0) है। जब (p(a)=0) हो तो (a) शून्यक कहलाता है।
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If (p(x)=x-3-2x), what is (p\(\sqrt{2}\))?
A. (0)
(\(\sqrt{2}\)3=2\sqrt{2}), so \(2\sqrt{2}-2\sqrt{2}=0\). Remember (\(\sqrt{a}\)3=a\sqrt{a}).
The correct answer is A. (0). (\(\sqrt{2}\)3=2\sqrt{2}), so \(2\sqrt{2}-2\sqrt{2}=0\). Remember (\(\sqrt{a}\)3=a\sqrt{a}).
(\(\sqrt{2}\)3=2\sqrt{2}), इसलिए \(2\sqrt{2}-2\sqrt{2}=0\) है। परीक्षा में (\(\sqrt{a}\)3=a\sqrt{a}) याद रखें।
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If \(x=2+\sqrt{5}\), what is the value of \(x^2-4x-1\)?
A. (0)
Since \(x-2=\sqrt{5}\), squaring gives ((x-2)2=5), so \(x^2-4x-1=0\). In exams square to remove the radical.
The correct answer is A. (0). Since \(x-2=\sqrt{5}\), squaring gives ((x-2)2=5), so \(x^2-4x-1=0\). In exams square to remove the radical.
\(x-2=\sqrt{5}\), इसलिए ((x-2)2=5) से \(x^2-4x-1=0\) मिलता है। परीक्षा में वर्ग करके अपरिमेय हटाएं।
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If (p(x)=x-2-2x-2), what is (p\(1+\sqrt{3}\))?
A. (0)
(\(1+\sqrt{3}\)2-2\(1+\sqrt{3}\)-2=1+2\sqrt{3}+3-2-2\sqrt{3}-2=0). Do not forget the middle term while expanding the square.
The correct answer is A. (0). (\(1+\sqrt{3}\)2-2\(1+\sqrt{3}\)-2=1+2\sqrt{3}+3-2-2\sqrt{3}-2=0). Do not forget the middle term while expanding the square.
(\(1+\sqrt{3}\)2-2\(1+\sqrt{3}\)-2=1+2\sqrt{3}+3-2-2\sqrt{3}-2=0)। वर्ग खोलते समय बीच का पद न भूलें।
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Which option is correct about the number (0)?
A. यह परिमेय और वास्तविक हैIt is rational and real
(0) can be written as \(\frac{0}{1}\) so it is rational. It also lies on the number line.
The correct answer is A. यह परिमेय और वास्तविक है / It is rational and real. (0) can be written as \(\frac{0}{1}\) so it is rational. It also lies on the number line.
\(0=\frac{0}{1}\) लिखा जा सकता है इसलिए यह परिमेय है। यह संख्या रेखा पर भी आता है।
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If (b) is an irrational number then what type of number is (b+0)?
A. अपरिमेय संख्याIrrational number
Adding (0) leaves the irrational number unchanged. Hence (b+0=b) is irrational.
The correct answer is A. अपरिमेय संख्या / Irrational number. Adding (0) leaves the irrational number unchanged. Hence (b+0=b) is irrational.
(0) जोड़ने से अपरिमेय संख्या वही रहती है। इसलिए (b+0=b) अपरिमेय है।
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If (a) is a rational number then what type of number is (a+0)?
A. परिमेय संख्याRational number
Adding (0) does not change the number. So (a+0=a) remains rational.
The correct answer is A. परिमेय संख्या / Rational number. Adding (0) does not change the number. So (a+0=a) remains rational.
(0) जोड़ने से संख्या नहीं बदलती। इसलिए (a+0=a) परिमेय रहेगा।
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Which option shows the result of multiplying an irrational number by zero?
A. (0) जो परिमेय है(0) which is rational
Multiplying any real number by (0) gives (0). (0) is a rational number.
The correct answer is A. (0) जो परिमेय है / (0) which is rational. Multiplying any real number by (0) gives (0). (0) is a rational number.
किसी भी वास्तविक संख्या को (0) से गुणा करने पर (0) मिलता है। (0) परिमेय संख्या है।
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A. परिमेय और वास्तविकRational and real
(0) can be written as \(\frac{0}{1}\) so it is rational. It is also a real number.
The correct answer is A. परिमेय और वास्तविक / Rational and real. (0) can be written as \(\frac{0}{1}\) so it is rational. It is also a real number.
\(0=\frac{0}{1}\) लिखा जा सकता है इसलिए यह परिमेय है। यह वास्तविक संख्या भी है।
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A. (x=9) शून्यक है(x=9) is a zero
((9,0)) lies on the (x)-axis so (p(9)=0). Moving from above to below also shows crossing.
The correct answer is A. (x=9) शून्यक है / (x=9) is a zero. ((9,0)) lies on the (x)-axis so (p(9)=0). Moving from above to below also shows crossing.
((9,0)) (x)-अक्ष पर है इसलिए (p(9)=0) है। ऊपर से नीचे जाना कटान को भी दिखाता है।
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In which situation will (x=3) be called a zero of polynomial (p(x))?
A. जब (p(3)=0)When (p(3)=0)
A zero is the (x)-value at which the polynomial value is zero. In exams check (p(a)=0).
The correct answer is A. जब (p(3)=0) / When (p(3)=0). A zero is the (x)-value at which the polynomial value is zero. In exams check (p(a)=0).
शून्यक वही (x)-मान है जिस पर बहुपद का मान शून्य हो। परीक्षा में (p(a)=0) जांचें।
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A polynomial graph meets the (x)-axis at ((7,0)). What is the value of (p(x)) at that point?
A. (0)
Every point on the (x)-axis has (y=0). Therefore (p(7)=0).
The correct answer is A. (0). Every point on the (x)-axis has (y=0). Therefore (p(7)=0).
(x)-अक्ष पर हर बिंदु का (y)-मान (0) होता है। इसलिए (p(7)=0) होगा।
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If a graph cuts the (x)-axis at ((0,0)), which conclusion is certain?
A. (0) बहुपद का शून्यक है(0) is a zero of the polynomial
Meeting at the origin shows (p(0)=0). It only confirms that (0) is a zero.
The correct answer is A. (0) बहुपद का शून्यक है / (0) is a zero of the polynomial. Meeting at the origin shows (p(0)=0). It only confirms that (0) is a zero.
मूल बिंदु पर मिलना (p(0)=0) बताता है। इससे केवल (0) का शून्यक होना निश्चित है।
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What is the (x)-intercept of the graph of (p(x)=3x+6)?
A. ((-2,0))
Solving (3x+6=0) gives (x=-2). The (y)-coordinate of an (x)-intercept is always (0).
The correct answer is A. ((-2,0)). Solving (3x+6=0) gives (x=-2). The (y)-coordinate of an (x)-intercept is always (0).
(3x+6=0) से (x=-2) मिलता है। (x)-प्रतिच्छेद का (y)-निर्देशांक हमेशा (0) होता है।
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The graph shows (p(2)=0). What is its geometrical meaning?
A. ग्राफ (x)-अक्ष को ((2,0)) पर मिलता हैThe graph meets the (x)-axis at ((2,0))
(p(2)=0) means (y=0) at (x=2). So the point lies on the (x)-axis.
The correct answer is A. ग्राफ (x)-अक्ष को ((2,0)) पर मिलता है / The graph meets the (x)-axis at ((2,0)). (p(2)=0) means (y=0) at (x=2). So the point lies on the (x)-axis.
(p(2)=0) का अर्थ (x=2) पर (y=0) है। इसलिए बिंदु (x)-अक्ष पर होगा।
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If (p(x)=x(x+6)4(x-3)5), what will be the graph behavior at (x=3)?
A. ग्राफ (x)-अक्ष को काटेगाThe graph will cross the (x)-axis
((x-3)5) is an odd-power factor, so the graph crosses at (x=3). Tip: at an odd power the graph usually crosses the axis.
The correct answer is A. ग्राफ (x)-अक्ष को काटेगा / The graph will cross the (x)-axis. ((x-3)5) is an odd-power factor, so the graph crosses at (x=3). Tip: at an odd power the graph usually crosses the axis.
((x-3)5) विषम घात का कारक है, इसलिए (x=3) पर कटान होगा। टिप: विषम घात में ग्राफ सामान्यतः अक्ष पार करता है।
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If (p(x)=x-2-2(b-4)x+(b-4)2), at which (x)-value will the graph touch the (x)-axis?
A. (x=b-4)
It is ((x-(b-4))2), so the repeated zero is (b-4). Tip: a perfect square form shows the zero quickly.
The correct answer is A. (x=b-4). It is ((x-(b-4))2), so the repeated zero is (b-4). Tip: a perfect square form shows the zero quickly.
यह ((x-(b-4))2) है इसलिए दोहराया शून्यक (b-4) है। टिप: पूर्ण वर्ग रूप में शून्यक तुरंत दिखता है।
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If (p(x)=x(x-7)4(x+2)3), what will be the graph behavior at (x=7)?
B. ग्राफ (x)-अक्ष को स्पर्श करेगाThe graph will touch the (x)-axis
((x-7)4) is an even-power factor, so the graph touches at (x=7). Tip: at an even power the graph usually turns back.
The correct answer is B. ग्राफ (x)-अक्ष को स्पर्श करेगा / The graph will touch the (x)-axis. ((x-7)4) is an even-power factor, so the graph touches at (x=7). Tip: at an even power the graph usually turns back.
((x-7)4) सम घात का कारक है, इसलिए (x=7) पर स्पर्श होगा। टिप: सम घात में ग्राफ आमतौर पर लौटता है।
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If (p(x)=x-2-2(a+3)x+(a+3)2), at which (x)-value will the graph touch the (x)-axis?
B. (x=a+3)
It is ((x-(a+3))2), so the repeated zero is (a+3). Tip: a perfect square form shows the zero quickly.
The correct answer is B. (x=a+3). It is ((x-(a+3))2), so the repeated zero is (a+3). Tip: a perfect square form shows the zero quickly.
यह ((x-(a+3))2) है, इसलिए दोहराया शून्यक (a+3) है। टिप: पूर्ण वर्ग रूप में शून्यक तुरंत दिखता है।
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If (p(x)=x(x+4)2(x-6)), what will be the graph behavior at (x=-4)?
B. ग्राफ (x)-अक्ष को स्पर्श करेगाThe graph will touch the (x)-axis
((x+4)2) is an even-power factor, so the graph touches at (x=-4). Tip: power (2) shows a repeated zero.
The correct answer is B. ग्राफ (x)-अक्ष को स्पर्श करेगा / The graph will touch the (x)-axis. ((x+4)2) is an even-power factor, so the graph touches at (x=-4). Tip: power (2) shows a repeated zero.
((x+4)2) सम घात का कारक है इसलिए (x=-4) पर स्पर्श होगा। टिप: घात (2) दोहराया शून्यक दिखाती है।
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If a graph touches the (y)-axis at ((0,0)), which conclusion about zeroes is correct?
A. (0) शून्यक है क्योंकि बिंदु (x)-अक्ष पर भी है(0) is a zero because the point is also on the (x)-axis
The origin lies on both axes, so (p(0)=0). Tip: treat ((0,0)) as a special point.
The correct answer is A. (0) शून्यक है क्योंकि बिंदु (x)-अक्ष पर भी है / (0) is a zero because the point is also on the (x)-axis. The origin lies on both axes, so (p(0)=0). Tip: treat ((0,0)) as a special point.
मूल बिंदु दोनों अक्षों पर होता है इसलिए (p(0)=0) है। टिप: ((0,0)) को विशेष बिंदु मानें।
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