medium se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
1071 questions tagged with medium.
What is the value of \(b^2+ac\) in \(7x^2-5x+2=0\)?
A. (39)
यहाँ (a=7), (b=-5), (c=2) हैं, इसलिए \(b^2+ac=25+14=39\) है। \(b^2\) में ऋण चिन्ह वर्ग के कारण धनात्मक हो जाता है। / Here (a=7), (b=-5), (c=2), so \(b^2+ac=25+14=39\). In \(b^2\), the negative sign becomes positive after squaring.
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If (x=4) is a root of \(x^2+sx-32=0\), what is the value of (s)?
A. (4)
(x=4) रखने पर (16+4s-32=0) मिलता है, इसलिए (s=4) है। मूल दिया हो तो सीधा प्रतिस्थापन करें। / Putting (x=4) gives (16+4s-32=0), so (s=4). When a root is given, substitute directly.
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What is the standard form of ((3x+4)2=7x+16)?
A. \(9x^2+17x=0\)
((3x+4)2=9x-2+24x+16) है। (7x+16) घटाने पर \(9x^2+17x=0\) मिलता है। / ((3x+4)2=9x-2+24x+16). Subtracting (7x+16) gives \(9x^2+17x=0\).
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In which perfect square form can \(x^2-18x+81=0\) be written?
A. ((x-9)2=0)
(x-2-18x+81=(x-9)2) होता है। पूर्ण वर्ग पहचानने के लिए मध्य पद (2ab) से मिलाएं। / (x-2-18x+81=(x-9)2). To identify a perfect square, match the middle term with (2ab).
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A. \(x^2-10x-21=0\)
क्षेत्रफल \(x^2\) है और दिया है \(x^2=10x+21\)। इसलिए \(x^2-10x-21=0\) सही है। / The area is \(x^2\), and it is given that \(x^2=10x+21\). Therefore \(x^2-10x-21=0\) is correct.
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If the roots of \(x^2+vx+28=0\) are (-4) and (-7), what is the value of (v)?
A. (11)
मूलों का योग (-11) है और \(x^2+vx+28=0\) में योग (-v) होता है। इसलिए (v=11) है। / The sum of roots is (-11), and in \(x^2+vx+28=0\), the sum is (-v). Therefore (v=11).
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Which pair of numbers is useful to identify the factors of \(x^2-17x+72=0\)?
A. (8) और (9)(8) and (9)
\(8\cdot9=72\) और (8+9=17) होता है। ऋण मध्य पद के कारण गुणनखंड ((x-8)(x-9)) बनते हैं। / \(8\cdot9=72\) and (8+9=17). Because the middle term is negative, the factors are ((x-8)(x-9)).
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If \(8x^2-32x+24=0\) is divided by (8), which simplified equation is obtained?
A. \(x^2-4x+3=0\)
हर पद को (8) से भाग देने पर \(x^2-4x+3=0\) मिलता है। समान अशून्य गुणनखंड से भाग देने पर मूल नहीं बदलते। / Dividing every term by (8) gives \(x^2-4x+3=0\). Dividing by a common nonzero factor does not change the roots.
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In which option is the constant term absent but the equation is quadratic?
A. \(2x^2+7x=0\)
\(2x^2+7x=0\) में \(x^2\) पद है और स्थिर पद अनुपस्थित है। स्थिर पद न होने पर भी समीकरण द्विघात हो सकता है। / In \(2x^2+7x=0\), the \(x^2\) term is present and the constant term is absent. An equation can be quadratic even without a constant term.
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In \(x^2+kx+81=0\), if the roots are equal and negative, which possible value of (k) is correct?
A. (18)
समान मूलों के लिए \(k^2=324\) और समान मूल \(-\frac{k}{2}\) होगा। ऋणात्मक मूल के लिए (k=18) सही है। / For equal roots, \(k^2=324\), and the equal root is \(-\frac{k}{2}\). For a negative root, (k=18) is correct.
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If the roots of \(x^2-18x+k=0\) are equal, what is (k)?
B. (81)
समान मूलों के लिए (D=0), इसलिए (324-4k=0) और (k=81)। समान मूल की शर्त में विवेचक शून्य रखें। / For equal roots, (D=0), so (324-4k=0) and (k=81). For equal roots, set the discriminant to zero.
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If \(x^2-15x+56=0\), what will the left side become when (x=7)?
A. (0)
\(7^2-15\cdot7+56=49-105+56=0\) है। बायां पक्ष (0) हो तो दिया मान मूल है। / \(7^2-15\cdot7+56=49-105+56=0\). If the left side becomes (0), the given value is a root.
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What is the standard form of ((x-4)(x+9)=5x)?
A. \(x^2-36=0\)
बाईं ओर \(x^2+5x-36\) मिलता है। (5x) घटाने पर \(x^2-36=0\) बनता है। / The left side gives \(x^2+5x-36\). Subtracting (5x) gives \(x^2-36=0\).
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Which quadratic equation is obtained by simplifying ((x+4)2-3(x+4)-10=0)?
A. \(x^2+5x-6=0\)
((x+4)2=x-2+8x+16) और (-3(x+4)=-3x-12) है। सरल करने पर \(x^2+5x-6=0\) मिलता है। / ((x+4)2=x-2+8x+16) and (-3(x+4)=-3x-12). Simplifying gives \(x^2+5x-6=0\).
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If the roots of \(x^2+ux+64=0\) are (8) and (8), what is the value of (u)?
B. (-16)
मूलों का योग (16) है और \(x^2+ux+64=0\) में योग (-u) होता है। इसलिए (u=-16) है। / The sum of roots is (16), and in \(x^2+ux+64=0\), the sum is (-u). Therefore (u=-16).
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Which pair is the correct roots of \(x^2-3x-40=0\)?
A. (8,-5)
((x-8)(x+5)=0) से मूल (8) और (-5) मिलते हैं। गुणनफल और योग दोनों मिलाकर जांचें। / From ((x-8)(x+5)=0), the roots are (8) and (-5). Check both product and sum.
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If the product of roots of \(qx^2-8x+12=0\) is (4), what is the value of (q)?
A. (3)
मूलों का गुणनफल \(\frac{12}{q}=4\), इसलिए (q=3) है। गुणनफल के लिए \(\frac{c}{a}\) का प्रयोग करें। / The product of roots is \(\frac{12}{q}=4\), so (q=3). Use \(\frac{c}{a}\) for the product of roots.
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If the sum of roots of \(4x^2+mx+20=0\) is (-6), what is (m)?
A. (24)
मूलों का योग \(-\frac{m}{4}=-6\), इसलिए (m=24) है। योग के सूत्र में ऋण चिन्ह न भूलें। / The sum of roots is \(-\frac{m}{4}=-6\), so (m=24). Do not forget the negative sign in the sum formula.
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What is the product of roots of \(6x^2+5x-14=0\)?
A. \(-\frac{7}{3}\)
मूलों का गुणनफल \(\frac{c}{a}=\frac{-14}{6}=-\frac{7}{3}\) है। उत्तर को सरल रूप में लिखें। / The product of roots is \(\frac{c}{a}=\frac{-14}{6}=-\frac{7}{3}\). Write the answer in simplified form.
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What is the sum of roots of \(5x^2-9x+4=0\)?
A. \(\frac{9}{5}\)
मूलों का योग \(-\frac{b}{a}=-\frac{-9}{5}=\frac{9}{5}\) है। सूत्र में (b) का चिन्ह ध्यान से रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-9}{5}=\frac{9}{5}\). Pay attention to the sign of (b) in the formula.
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Which quadratic equation has sum of roots (-8) and product (15)?
A. \(x^2+8x+15=0\)
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। योग (-8) रखने पर \(x^2+8x+15=0\) मिलता है। \(/ A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-8) gives (x^2+8x+15=0).\)
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If the roots are (-4) and (-9), what is the product of the roots?
A. (36)
मूलों का गुणनफल ((-4)(-9)=36) है। दो ऋणात्मक संख्याओं का गुणनफल धनात्मक होता है। / The product of roots is ((-4)(-9)=36). The product of two negative numbers is positive.
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If (x=-6) and (x=1) are roots, what is the sum of the roots?
A. (-5)
मूलों का योग (-6+1=-5) है। विपरीत चिन्ह वाली संख्याओं में बड़े परिमाण का चिन्ह आता है। / The sum of roots is (-6+1=-5). For numbers with opposite signs, the sign of the larger magnitude is used.
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What is the value of (b) in \(x^2+6\sqrt{5}x+45=0\)?
A. \(6\sqrt{5}\)
(x) के साथ लगा गुणांक \(6\sqrt{5}\) है। करणी वाले गुणांक भी चिन्ह सहित लिखें। / The coefficient attached to (x) is \(6\sqrt{5}\). Write radical coefficients with their signs too.
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Which option is not a usual quadratic equation?
C. \(\frac{1}{x^2}+x+2=0\)
\(\frac{1}{x^2}=x^{-2}\) है, जो बहुपद रूप नहीं है। सामान्य द्विघात समीकरण में चर की ऋणात्मक घात नहीं होती। / \(\frac{1}{x^2}=x^{-2}\), which is not polynomial form. A usual quadratic equation does not have a negative power of the variable.
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What is the form with integer coefficients for \(\frac{3}{4}x^2-\frac{1}{2}x+2=0\)?
A. \(3x^2-2x+8=0\)
हर हटाने के लिए पूरे समीकरण को (4) से गुणा करें। इससे \(3x^2-2x+8=0\) मिलता है। / Multiply the whole equation by (4) to remove the denominators. This gives \(3x^2-2x+8=0\).
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How will \(\frac{x^2}{5}+2x-7=0\) be written without fractions?
A. \(x^2+10x-35=0\)
पूरे समीकरण को (5) से गुणा करने पर \(x^2+10x-35=0\) मिलता है। भिन्न हटाने के लिए पूरे समीकरण पर गुणा करें। / Multiplying the whole equation by (5) gives \(x^2+10x-35=0\). To remove fractions, multiply the whole equation.
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What is the value of (ac) in \(4x^2+13x+3=0\)?
A. (12)
यहाँ (a=4) और (c=3), इसलिए (ac=12) है। मध्य पद विभाजन में (ac) उपयोगी होता है। / Here (a=4) and (c=3), so (ac=12). The value (ac) is useful in splitting the middle term.
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Which factor form can represent \(x^2+11x+30=0\)?
A. ((x+5)(x+6)=0)
\(5\cdot6=30\) और (5+6=11) है। इसलिए सही गुणनखंड ((x+5)(x+6)) हैं। / \(5\cdot6=30\) and (5+6=11). Therefore the correct factors are ((x+5)(x+6)).
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What are the roots of \(49x^2-64=0\)?
A. \(x=\pm \frac{8}{7}\)
\(49x^2=64\), इसलिए \(x^2=\frac{64}{49}\) और \(x=\pm\frac{8}{7}\) है। वर्गमूल लेते समय दोनों चिन्ह लें। / \(49x^2=64\), so \(x^2=\frac{64}{49}\) and \(x=\pm\frac{8}{7}\). Take both signs while taking square roots.
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