A. दूसरा (7), कटान ((6,0)), ((7,0))/Other (7), intersections ((6,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0)). In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (13) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
A. दूसरा (7), कटान ((4,0)), ((7,0))/Other (7), intersections ((4,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0)). In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (11) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
A. दूसरा (3), कटान ((2,0)), ((3,0))/Other (3), intersections ((2,0)), ((3,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0)). In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (5) है, इसलिए दूसरा शून्यक (3) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 3
Exam Tip
(x)-अक्ष से प्रत्येक अलग कटाव एक वास्तविक शून्यक देता है। दो कटाव होने पर दो वास्तविक शून्यक होंगे।
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।
The related equation has (D=4k-2-4\(k^2+9\)=-36). So the graph does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. कोई प्रतिच्छेद नहीं / No intersection. The related equation has (D=4k-2-4\(k^2+9\)=-36). So the graph does not cut the (x)-axis.
Step 3
Exam Tip
संबंधित समीकरण का (D=4k-2-4\(k^2+9\)=-36) है। इसलिए ग्राफ (x)-अक्ष को नहीं काटता।
The related equation has (D=4k-2-4\(k^2+4\)=-16). So the graph does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. कोई प्रतिच्छेद नहीं / No intersection. The related equation has (D=4k-2-4\(k^2+4\)=-16). So the graph does not cut the (x)-axis.
Step 3
Exam Tip
संबंधित समीकरण का (D=4k-2-4\(k^2+4\)=-16) है। इसलिए ग्राफ (x)-अक्ष को नहीं काटता।
The related equation has (D=4k-2-4\(k^2+1\)=-4). So the graph does not cut the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. कोई प्रतिच्छेद नहीं / No intersection. The related equation has (D=4k-2-4\(k^2+1\)=-4). So the graph does not cut the (x)-axis.
Step 3
Exam Tip
संबंधित समीकरण का (D=4k-2-4\(k^2+1\)=-4) है। इसलिए ग्राफ (x)-अक्ष को नहीं काटता।
(x-4-1296=\(x^2-36\)\(x^2+36\)), and the real zeroes are only \(\pm6\). Tip: \(x^2+36\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-6,0)) और ((6,0)) / ((-6,0)) and ((6,0)). (x-4-1296=\(x^2-36\)\(x^2+36\)), and the real zeroes are only \(\pm6\). Tip: \(x^2+36\) gives no real zero.
Step 3
Exam Tip
(x-4-1296=\(x^2-36\)\(x^2+36\)) है और वास्तविक शून्यक केवल \(\pm6\) हैं। टिप: \(x^2+36\) वास्तविक शून्यक नहीं देता।
A. (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\))/(\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\))
Step 1
Concept
From \(36x^2-49=0\), \(x=\pm\frac{7}{6}\). Tip: treat \(36x^2\) as ((6x)2).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\)) / (\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\)). From \(36x^2-49=0\), \(x=\pm\frac{7}{6}\). Tip: treat \(36x^2\) as ((6x)2).
Step 3
Exam Tip
\(36x^2-49=0\) से \(x=\pm\frac{7}{6}\) मिलता है। टिप: \(36x^2\) को ((6x)2) समझें।
(x-2-13x-68=(x-17)(x+4)), so the zeroes are (17) and (-4). Tip: write intersection points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((17,0)) और ((-4,0)) / ((17,0)) and ((-4,0)). (x-2-13x-68=(x-17)(x+4)), so the zeroes are (17) and (-4). Tip: write intersection points from factors.
Step 3
Exam Tip
(x-2-13x-68=(x-17)(x+4)) है, इसलिए शून्यक (17) और (-4) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।
The polynomial is ((x-n)(x-(n+3))), so the zeroes are (n) and (n+3). Tip: write zeroes as ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((n,0)) और ((n+3,0)) / ((n,0)) and ((n+3,0)). The polynomial is ((x-n)(x-(n+3))), so the zeroes are (n) and (n+3). Tip: write zeroes as ((x,0)).
Step 3
Exam Tip
बहुपद ((x-n)(x-(n+3))) है इसलिए शून्यक (n) और (n+3) हैं। टिप: शून्यकों को ((x,0)) में लिखें।
(x-4-625=\(x^2-25\)\(x^2+25\)), and the real zeroes are only \(\pm5\). Tip: \(x^2+25\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-5,0)) और ((5,0)) / ((-5,0)) and ((5,0)). (x-4-625=\(x^2-25\)\(x^2+25\)), and the real zeroes are only \(\pm5\). Tip: \(x^2+25\) gives no real zero.
Step 3
Exam Tip
(x-4-625=\(x^2-25\)\(x^2+25\)) है और वास्तविक शून्यक केवल \(\pm5\) हैं। टिप: \(x^2+25\) वास्तविक शून्यक नहीं देता।
A. (\left\(\frac{6}{5},0\right\)) और (\left\(-\frac{6}{5},0\right\))/(\left\(\frac{6}{5},0\right\)) and (\left\(-\frac{6}{5},0\right\))
Step 1
Concept
From \(25x^2-36=0\), \(x=\pm\frac{6}{5}\). Tip: treat \(25x^2\) as ((5x)2).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{6}{5},0\right\)) और (\left\(-\frac{6}{5},0\right\)) / (\left\(\frac{6}{5},0\right\)) and (\left\(-\frac{6}{5},0\right\)). From \(25x^2-36=0\), \(x=\pm\frac{6}{5}\). Tip: treat \(25x^2\) as ((5x)2).
Step 3
Exam Tip
\(25x^2-36=0\) से \(x=\pm\frac{6}{5}\) मिलता है। टिप: \(25x^2\) को ((5x)2) समझें।
(x-2-9x-52=(x-13)(x+4)), so the zeroes are (13) and (-4). Tip: write intersection points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((13,0)) और ((-4,0)) / ((13,0)) and ((-4,0)). (x-2-9x-52=(x-13)(x+4)), so the zeroes are (13) and (-4). Tip: write intersection points from factors.
Step 3
Exam Tip
(x-2-9x-52=(x-13)(x+4)) है, इसलिए शून्यक (13) और (-4) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।
The polynomial is ((x-m)(x-(m-1))), so the zeroes are (m) and (m-1). Tip: write zeroes as ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((m,0)) और ((m-1,0)) / ((m,0)) and ((m-1,0)). The polynomial is ((x-m)(x-(m-1))), so the zeroes are (m) and (m-1). Tip: write zeroes as ((x,0)).
Step 3
Exam Tip
बहुपद ((x-m)(x-(m-1))) है, इसलिए शून्यक (m) और (m-1) हैं। टिप: शून्यकों को ((x,0)) में लिखें।
(x-4-81=\(x^2-9\)\(x^2+9\)), and the real zeroes are only \(\pm3\). Tip: \(x^2+9\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0)). (x-4-81=\(x^2-9\)\(x^2+9\)), and the real zeroes are only \(\pm3\). Tip: \(x^2+9\) gives no real zero.
Step 3
Exam Tip
(x-4-81=\(x^2-9\)\(x^2+9\)) है और वास्तविक शून्यक केवल \(\pm3\) हैं। टिप: \(x^2+9\) वास्तविक शून्यक नहीं देता।
A. (\left\(\frac{3}{4},0\right\)) और (\left\(-\frac{3}{4},0\right\))/(\left\(\frac{3}{4},0\right\)) and (\left\(-\frac{3}{4},0\right\))
Step 1
Concept
From \(16x^2-9=0\), \(x=\pm\frac{3}{4}\). Tip: treat \(16x^2\) as ((4x)2).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{3}{4},0\right\)) और (\left\(-\frac{3}{4},0\right\)) / (\left\(\frac{3}{4},0\right\)) and (\left\(-\frac{3}{4},0\right\)). From \(16x^2-9=0\), \(x=\pm\frac{3}{4}\). Tip: treat \(16x^2\) as ((4x)2).
Step 3
Exam Tip
\(16x^2-9=0\) से \(x=\pm\frac{3}{4}\) मिलता है। टिप: \(16x^2\) को ((4x)2) समझें।
The zeroes are (m), (n), (r), so the mean is \(\frac{m+n+r}{3}\). Tip: take the first coordinate even in symbolic points.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{m+n+r}{3}\). The zeroes are (m), (n), (r), so the mean is \(\frac{m+n+r}{3}\). Tip: take the first coordinate even in symbolic points.
Step 3
Exam Tip
शून्यक (m), (n), (r) हैं इसलिए माध्य \(\frac{m+n+r}{3}\) है। टिप: प्रतीकात्मक बिंदुओं में भी पहला निर्देशांक लें।
(x-2-8x-33=(x-11)(x+3)), so the zeroes are (11) and (-3). Tip: form ((x,0)) points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((11,0)) और ((-3,0)) / ((11,0)) and ((-3,0)). (x-2-8x-33=(x-11)(x+3)), so the zeroes are (11) and (-3). Tip: form ((x,0)) points from factors.
Step 3
Exam Tip
(x-2-8x-33=(x-11)(x+3)) है इसलिए शून्यक (11) और (-3) हैं। टिप: गुणनखंडों से बिंदु ((x,0)) बनाएं।
It is ((x-u)(x-v)), so the zeroes are (u) and (v). Tip: write each zero as the point ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((u,0)) और ((v,0)) / ((u,0)) and ((v,0)). It is ((x-u)(x-v)), so the zeroes are (u) and (v). Tip: write each zero as the point ((x,0)).
Step 3
Exam Tip
यह ((x-u)(x-v)) है इसलिए शून्यक (u) और (v) हैं। टिप: शून्यक को ((x,0)) बिंदु के रूप में लिखें।
(x-4-16=\(x^2-4\)\(x^2+4\)), and the real zeroes are only \(\pm2\). Tip: \(x^2+4\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-2,0)) और ((2,0)) / ((-2,0)) and ((2,0)). (x-4-16=\(x^2-4\)\(x^2+4\)), and the real zeroes are only \(\pm2\). Tip: \(x^2+4\) gives no real zero.
Step 3
Exam Tip
(x-4-16=\(x^2-4\)\(x^2+4\)) है और वास्तविक शून्यक केवल \(\pm2\) हैं। टिप: \(x^2+4\) वास्तविक शून्यक नहीं देता।
A. (\left\(\frac{4}{3},0\right\)) और (\left\(-\frac{4}{3},0\right\))/(\left\(\frac{4}{3},0\right\)) and (\left\(-\frac{4}{3},0\right\))
Step 1
Concept
From \(9x^2-16=0\), \(x=\pm\frac{4}{3}\). Tip: treat \(9x^2\) as ((3x)2).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{4}{3},0\right\)) और (\left\(-\frac{4}{3},0\right\)) / (\left\(\frac{4}{3},0\right\)) and (\left\(-\frac{4}{3},0\right\)). From \(9x^2-16=0\), \(x=\pm\frac{4}{3}\). Tip: treat \(9x^2\) as ((3x)2).
Step 3
Exam Tip
\(9x^2-16=0\) से \(x=\pm\frac{4}{3}\) मिलता है। टिप: \(9x^2\) को ((3x)2) समझें।
The zeroes are (a), (b), (c), so their product is (abc). Tip: even in symbolic points, the first coordinate is the zero.
Step 2
Why this answer is correct
The correct answer is B. (abc). The zeroes are (a), (b), (c), so their product is (abc). Tip: even in symbolic points, the first coordinate is the zero.
Step 3
Exam Tip
शून्यक (a), (b), (c) हैं, इसलिए गुणनफल (abc) है। टिप: प्रतीकात्मक बिंदु में भी पहला निर्देशांक शून्यक है।
(x-2-4x-21=(x-7)(x+3)), so the zeroes are (7) and (-3). Tip: form ((x,0)) points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((7,0)) और ((-3,0)) / ((7,0)) and ((-3,0)). (x-2-4x-21=(x-7)(x+3)), so the zeroes are (7) and (-3). Tip: form ((x,0)) points from factors.
Step 3
Exam Tip
(x-2-4x-21=(x-7)(x+3)) है, इसलिए शून्यक (7) और (-3) हैं। टिप: गुणनखंडों से बिंदु ((x,0)) बनाएं।
(x-4-1=\(x^2-1\)\(x^2+1\)), and the real zeroes are only \(\pm1\). Tip: \(x^2+1\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-1,0)) और ((1,0)) / ((-1,0)) and ((1,0)). (x-4-1=\(x^2-1\)\(x^2+1\)), and the real zeroes are only \(\pm1\). Tip: \(x^2+1\) gives no real zero.
Step 3
Exam Tip
(x-4-1=\(x^2-1\)\(x^2+1\)) है और वास्तविक शून्यक केवल \(\pm1\) हैं। टिप: \(x^2+1\) वास्तविक शून्यक नहीं देता।
A. (\left\(\frac{5}{2},0\right\)) और (\left\(-\frac{5}{2},0\right\))/(\left\(\frac{5}{2},0\right\)) and (\left\(-\frac{5}{2},0\right\))
Step 1
Concept
From \(4x^2-25=0\), \(x=\pm\frac{5}{2}\). Tip: treat \(4x^2\) as ((2x)2).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{5}{2},0\right\)) और (\left\(-\frac{5}{2},0\right\)) / (\left\(\frac{5}{2},0\right\)) and (\left\(-\frac{5}{2},0\right\)). From \(4x^2-25=0\), \(x=\pm\frac{5}{2}\). Tip: treat \(4x^2\) as ((2x)2).
Step 3
Exam Tip
\(4x^2-25=0\) से \(x=\pm\frac{5}{2}\) मिलता है। टिप: \(4x^2\) को ((2x)2) समझें।
(x-2+2x-15=(x+5)(x-3)), so the zeroes are (-5) and (3). Tip: form points ((x,0)) from factors.
Step 2
Why this answer is correct
The correct answer is A. ((3,0)) और ((-5,0)) / ((3,0)) and ((-5,0)). (x-2+2x-15=(x+5)(x-3)), so the zeroes are (-5) and (3). Tip: form points ((x,0)) from factors.
Step 3
Exam Tip
(x-2+2x-15=(x+5)(x-3)), इसलिए शून्यक (-5) और (3) हैं। टिप: गुणनखंडों से बिंदु ((x,0)) बनाएं।
The polynomial equals ((x-a)(x-b)), so the zeroes are (a) and (b). Tip: connect factor form with graph intersections.
Step 2
Why this answer is correct
The correct answer is A. ((a,0)) और ((b,0)) / ((a,0)) and ((b,0)). The polynomial equals ((x-a)(x-b)), so the zeroes are (a) and (b). Tip: connect factor form with graph intersections.
Step 3
Exam Tip
बहुपद ((x-a)(x-b)) के बराबर है, इसलिए शून्यक (a) और (b) हैं। टिप: गुणनखंड रूप को ग्राफ कटान से जोड़ें।
(x-2-3x-10=(x-5)(x+2)), so the zeroes are (5) and (-2). Tip: write intersection points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((5,0)) और ((-2,0)) / ((5,0)) and ((-2,0)). (x-2-3x-10=(x-5)(x+2)), so the zeroes are (5) and (-2). Tip: write intersection points from factors.
Step 3
Exam Tip
(x-2-3x-10=(x-5)(x+2)) इसलिए शून्यक (5) और (-2) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।
B. कटान नहीं बदलते/The intersections do not change
Step 1
Concept
A non-zero constant multiplier does not change zeroes. Tip: zeroes come from factors that make the value zero.
Step 2
Why this answer is correct
The correct answer is B. कटान नहीं बदलते / The intersections do not change. A non-zero constant multiplier does not change zeroes. Tip: zeroes come from factors that make the value zero.
Step 3
Exam Tip
अशून्य स्थिर गुणक शून्यकों को नहीं बदलता। टिप: शून्यक केवल शून्य बनाने वाले कारकों से मिलते हैं।
The axis of symmetry passes through the average \(x=\frac{1+7}{2}=4\). Tip: the middle of two zeroes is useful in a parabola.
Step 2
Why this answer is correct
The correct answer is B. (x=4). The axis of symmetry passes through the average \(x=\frac{1+7}{2}=4\). Tip: the middle of two zeroes is useful in a parabola.
Step 3
Exam Tip
सममिति अक्ष शून्यकों के औसत \(x=\frac{1+7}{2}=4\) से गुजरता है। टिप: परवलय में दो शून्यकों का मध्य उपयोगी है।
An (x)-axis intersection occurs where (p(x)=0). Tip: (p(2)=5) does not give a zero.
Step 2
Why this answer is correct
The correct answer is A. ((-3,0)) और ((8,0)) / ((-3,0)) and ((8,0)). An (x)-axis intersection occurs where (p(x)=0). Tip: (p(2)=5) does not give a zero.
Step 3
Exam Tip
जहाँ (p(x)=0) है वहीं (x)-अक्ष कटान होता है। टिप: (p(2)=5) शून्यक नहीं देता।
(x-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). Tip: factor and then write intersection points.
Step 2
Why this answer is correct
The correct answer is A. ((3,0)) और ((4,0)) / ((3,0)) and ((4,0)). (x-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). Tip: factor and then write intersection points.
Step 3
Exam Tip
(x-2-7x+12=(x-3)(x-4)) इसलिए शून्यक (3) और (4) हैं। टिप: गुणनखंड बनाकर कटान बिंदु लिखें।
The first coordinates of intersection points are the zeroes. Tip: choose points whose second coordinate is (0).
Step 2
Why this answer is correct
The correct answer is B. (-8) और (3) / (-8) and (3). The first coordinates of intersection points are the zeroes. Tip: choose points whose second coordinate is (0).
Step 3
Exam Tip
कटान बिंदुओं के पहले निर्देशांक शून्यक होते हैं। टिप: दूसरे निर्देशांक को (0) देखकर बिंदु चुनें।
The first coordinate of each intersection point is a zero. Tip: read the zero (a) from ((a,0)).
Step 2
Why this answer is correct
The correct answer is B. शून्यक (a,b,c) हैं / The zeroes are (a,b,c). The first coordinate of each intersection point is a zero. Tip: read the zero (a) from ((a,0)).
Step 3
Exam Tip
हर कटान बिंदु का पहला निर्देशांक शून्यक है। टिप: ((a,0)) से शून्यक (a) पढ़ें।
The zeroes are (r) and (s), so the average is \(\frac{r+s}{2}\). Tip: divide the sum by the number of values.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{r+s}{2}\). The zeroes are (r) and (s), so the average is \(\frac{r+s}{2}\). Tip: divide the sum by the number of values.
Step 3
Exam Tip
शून्यक (r) और (s) हैं, इसलिए औसत \(\frac{r+s}{2}\) है। टिप: औसत में योग को संख्या से भाग दें।
Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((4,0)) और ((-2,0)) / ((4,0)) and ((-2,0)). Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).
Step 3
Exam Tip
कारकों को शून्य करने पर (x=4) और (x=-2) मिलते हैं। टिप: शून्यक को ((x,0)) बिंदु में बदलें।
A. वास्तविक शून्यकों की संख्या जानना/To know the number of real zeroes
Step 1
Concept
The (x)-axis intersections tell the number of real zeroes. Tip: first count intersections from the graph.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या जानना / To know the number of real zeroes. The (x)-axis intersections tell the number of real zeroes. Tip: first count intersections from the graph.
Step 3
Exam Tip
(x)-अक्ष कटान वास्तविक शून्यकों की संख्या बताते हैं। टिप: ग्राफ से पहले कटान गिनें।
A. वास्तविक शून्यकों की संख्या/Number of real zeroes
Step 1
Concept
The number of distinct times the graph meets the (x)-axis gives the number of real zeroes. Check this first while reading a graph.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या / Number of real zeroes. The number of distinct times the graph meets the (x)-axis gives the number of real zeroes. Check this first while reading a graph.
Step 3
Exam Tip
ग्राफ जितनी बार (x)-अक्ष से अलग-अलग मिलता है, उतने वास्तविक शून्यक होते हैं। इसे ग्राफ पढ़ते समय सबसे पहले देखें।
B. लंबे ऐतिहासिक समय को दर्ज करने के लिए/To record long historical time
Step 1
Concept
The Long Count system helped record long dates and royal events. For exams treat Maya chronology as advanced.
Step 2
Why this answer is correct
The correct answer is B. लंबे ऐतिहासिक समय को दर्ज करने के लिए / To record long historical time. The Long Count system helped record long dates and royal events. For exams treat Maya chronology as advanced.
Step 3
Exam Tip
लंबी गणना प्रणाली लंबी तिथियों और राजकीय घटनाओं को दर्ज करने में सहायक थी। परीक्षा में माया कालगणना को उन्नत मानें।
A. लंबी अवधि की तिथि गणना और खगोलीय समझ/Long-term date reckoning and astronomical understanding
Step 1
Concept
The Long Count calendar is famous for long-term date reckoning. Link it with Maya mathematics and astronomy.
Step 2
Why this answer is correct
The correct answer is A. लंबी अवधि की तिथि गणना और खगोलीय समझ / Long-term date reckoning and astronomical understanding. The Long Count calendar is famous for long-term date reckoning. Link it with Maya mathematics and astronomy.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी तिथि गणना के लिए प्रसिद्ध है। परीक्षा में इसे माया गणित और खगोल से जोड़ें।
A. लंबी अवधि की तिथि गणना/Long-term date reckoning
Step 1
Concept
The Long Count calendar was useful for long date reckoning. Link it with Maya mathematics and astronomy.
Step 2
Why this answer is correct
The correct answer is A. लंबी अवधि की तिथि गणना / Long-term date reckoning. The Long Count calendar was useful for long date reckoning. Link it with Maya mathematics and astronomy.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी तिथि गणना में उपयोगी था। परीक्षा में इसे माया गणित और खगोल ज्ञान से जोड़ें।
The Long Count calendar was useful for recording long periods of dates. Link it with Maya astronomy and calculation.
Step 2
Why this answer is correct
The correct answer is A. लंबे समय की तिथि गणना / Long term date reckoning. The Long Count calendar was useful for recording long periods of dates. Link it with Maya astronomy and calculation.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी अवधि की तिथियों को दर्ज करने के लिए उपयोगी था। परीक्षा में इसे माया खगोल और गणना से जोड़ें।
A. लंबे समय की तिथियों को दर्ज करने के लिए/Recording long periods of dates
Step 1
Concept
The Long Count calendar was useful for long date reckoning. Connect it with Maya mathematics and astronomy.
Step 2
Why this answer is correct
The correct answer is A. लंबे समय की तिथियों को दर्ज करने के लिए / Recording long periods of dates. The Long Count calendar was useful for long date reckoning. Connect it with Maya mathematics and astronomy.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी तिथि गणना के लिए उपयोगी था। परीक्षा में इसे माया गणना और खगोल ज्ञान से जोड़ें।
The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 2
Why this answer is correct
The correct answer is A. \(1-\sqrt{3}\). The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 3
Exam Tip
शून्यकों का योग (2) है, इसलिए दूसरा शून्यक (2-\(1+\sqrt{3}\)=1-\sqrt{3}) है। परिमेय गुणांकों में संयुग्मी भी मिलता है।
The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (11). The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (5) है इसलिए दूसरा शून्यक (11) होगा। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-9). The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (-2) है, इसलिए दूसरा शून्यक (-9) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य से जोड़ें।
A. दूसरा (5), कटान ((4,0)), ((5,0))/Other (5), intersections ((4,0)), ((5,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0)). In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (9) है इसलिए दूसरा शून्यक (5) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (3) है इसलिए दूसरा शून्यक (-5) होगा। टिप: \(\frac{a+b}{2}\) को सममिति अक्ष के बराबर रखें।
The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (10). The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दोनों शून्यकों का औसत (4) है इसलिए दूसरा शून्यक (10) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य मान से जोड़ें।
A. दूसरा (4), कटान ((3,0)), ((4,0))/Other (4), intersections ((3,0)), ((4,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0)). In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (7) है, इसलिए दूसरा शून्यक (4) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (2) है, इसलिए दूसरा शून्यक (-5) होगा। टिप: \( \frac{a+b}{2} \) को सममिति अक्ष के बराबर रखें।
The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is C. (7). The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (1) होगा इसलिए दूसरा शून्यक (7) है। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 3
Exam Tip
केवल एक (x)-अक्ष कटान दिख रहा है इसलिए एक वास्तविक शून्यक है। टिप: संख्या बिंदुओं की गिनती से आती है।
For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 2
Why this answer is correct
The correct answer is A. \(2-\sqrt{3}\). For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 3
Exam Tip
परिमेय गुणांकों वाले द्विघात में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी मूल का नियम उपयोगी है।
A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\)/Other \(\sqrt{5}\), \(k=\sqrt{5}\)
Step 1
Concept
The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\). The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 3
Exam Tip
गुणनफल (5) है, इसलिए दूसरा शून्यक \(\frac{5}{\sqrt{5}}=\sqrt{5}\) होगा। योग \(2\sqrt{5}=2k\), अतः \(k=\sqrt{5}\) है।
The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-1). The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (8) है और औसत \(\frac{-10+8}{2}=-1\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-2). The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (4) है और औसत \(\frac{-8+4}{2}=-2\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 2
Why this answer is correct
The correct answer is A. (7). The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (2) होगा, इसलिए दूसरा शून्यक (7) है। टिप: परवलय में सममिति अक्ष शून्यकों के मध्य से गुजरता है।
