product of zeroes se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
16 questions tagged with product of zeroes.
A. (22)
गुणनफल (\(5+\sqrt{3}\)\(5-\sqrt{3}\)=25-3=22) है। परीक्षा में ((a+b)(a-b)=a-2-b-2) याद रखें। / The product is (\(5+\sqrt{3}\)\(5-\sqrt{3}\)=25-3=22). In exams remember ((a+b)(a-b)=a-2-b-2).
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If (p(x)=x-2-2x-3\sqrt{2}), what does the constant term tell about the zeroes?
A. शून्यकों का गुणनफल \(-3\sqrt{2}\) हैThe product of zeroes is \(-3\sqrt{2}\)
एकक द्विघात में स्थिर पद शून्यकों का गुणनफल होता है। यहाँ \(\alpha\beta=-3\sqrt{2}\) है। / In a monic quadratic, the constant term is the product of zeroes. Here \(\alpha\beta=-3\sqrt{2}\).
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If one zero of (p(x)=x-2-2kx+5) is \(\sqrt{5}\), what will be the other zero and (k)?
A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\)Other \(\sqrt{5}\), \(k=\sqrt{5}\)
गुणनफल (5) है, इसलिए दूसरा शून्यक \(\frac{5}{\sqrt{5}}=\sqrt{5}\) होगा। योग \(2\sqrt{5}=2k\), अतः \(k=\sqrt{5}\) है। / The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
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If (p(x)=x-2-10x+1), what type of number is the product of its zeroes?
B. परिमेयRational
गुणनफल \(\frac{c}{a}=\frac{1}{1}=1\) है, जो परिमेय है। शून्यक अपरिमेय हो सकते हैं पर उनका गुणनफल परिमेय हो सकता है। / The product is \(\frac{c}{a}=\frac{1}{1}=1\), which is rational. Zeroes may be irrational but their product can be rational.
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If (p(x)=\sqrt{3}x-2-6x+2\sqrt{3}), what is the product of its zeroes?
A. (2)
गुणनफल \(\frac{c}{a}=\frac{2\sqrt{3}}{\sqrt{3}}=2\) है। समान करणी कट सकती है। / The product is \(\frac{c}{a}=\frac{2\sqrt{3}}{\sqrt{3}}=2\). Like radicals can cancel.
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If (p(x)=x-2-3x+\sqrt{2}), what is the product of its zeroes?
A. \(\sqrt{2}\)
गुणनफल \(\frac{c}{a}\) होता है। यहाँ \(c=\sqrt{2}\) और (a=1), इसलिए गुणनफल \(\sqrt{2}\) है। / The product is \(\frac{c}{a}\). Here \(c=\sqrt{2}\) and (a=1), so the product is \(\sqrt{2}\).
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If (p(x)=x-2-2x-2), what is the product of its zeroes?
A. (-2)
द्विघात में गुणनफल \(\frac{c}{a}\) होता है। यहाँ \(\frac{-2}{1}=-2\) है। / In a quadratic, the product is \(\frac{c}{a}\). Here it is \(\frac{-2}{1}=-2\).
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If zeroes of (p(x)=x-2-6x+n) are \(3+\sqrt{m}\) and \(3-\sqrt{m}\), and (n=5), what is (m)?
A. (4)
गुणनफल (9-m) है और वह (n=5) के बराबर है। अतः (9-m=5), इसलिए (m=4)। / The product is (9-m), and it equals (n=5). Thus (9-m=5), so (m=4).
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If (p(x)=x-2-2\sqrt{3}x+2), what is the product of its zeroes?
A. (2)
द्विघात \(ax^2+bx+c\) में शून्यकों का गुणनफल \(\frac{c}{a}\) होता है। यहाँ \(\frac{2}{1}=2\) है। / In \(ax^2+bx+c\), the product of zeroes is \(\frac{c}{a}\). Here it is \(\frac{2}{1}=2\).
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For which value of (k) will (p(x)=x-2-10x+k) have zeroes \(5+\sqrt{2}\) and \(5-\sqrt{2}\)?
A. (23)
गुणनफल (\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23) है। इसलिए (k=23) होगा। / The product is (\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23). So (k=23).
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A. (-66)
शून्यक (11) और (-6) हैं, इसलिए गुणनफल (-66) है। टिप: स्पर्श बिंदु भी शून्यक होता है। / The zeroes are (11) and (-6), so the product is (-66). Tip: a touching point is also a zero.
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A. (-45)
शून्यक (9) और (-5) हैं, इसलिए गुणनफल (-45) है। टिप: स्पर्श बिंदु भी शून्यक होता है। / The zeroes are (9) and (-5), so the product is (-45). Tip: a touching point is also a zero.
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If (p(-6)=0), (p(-1)>0), (p(4)=0) and (p(7)<0), what is the product of the given zeroes?
A. (-24)
दिए गए शून्यक (-6) और (4) हैं, इसलिए गुणनफल (-24) है। टिप: केवल (p(x)=0) वाले (x)-मान लें। / The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).
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B. (0)
शून्यक (0) और (a) हैं, इसलिए गुणनफल (0) है। टिप: (0) शामिल हो तो गुणनफल (0) होगा। / The zeroes are (0) and (a), so the product is (0). Tip: if (0) is included, the product is (0).
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B. (-72)
शून्यक (-4), (2), (9) हैं और गुणनफल (-72) है। टिप: केवल (x)-निर्देशांकों को गुणा करें। / The zeroes are (-4), (2), (9), and their product is (-72). Tip: multiply only the (x)-coordinates.
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If a graph cuts the (x)-axis at ((-6,0)) and ((2,0)), what is the product of zeroes?
C. (-12)
शून्यक (-6) और (2) हैं, इसलिए गुणनफल (-12) है। टिप: (y)-निर्देशांक को गुणन में शामिल न करें। / The zeroes are (-6) and (2), so the product is (-12). Tip: do not include the (y)-coordinate in the product.
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