sum of roots se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
55 questions tagged with sum of roots.
If the roots of (x-2-(m+2)x+12=0) are (3) and (4), what is the value of (m)?
A. (5)
मूलों का योग (3+4=7) है। इसलिए (m+2=7) और (m=5) होगा। / The sum of roots is (3+4=7). Therefore (m+2=7), so (m=5).
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If \(\alpha\) and \(\beta\) are roots of \(4x^2-20x+7=0\), what is \(\alpha+\beta\)?
A. (5)
मूलों का योग \(-\frac{b}{a}=-\frac{-20}{4}=5\) है। सूत्र में (b) का चिन्ह सही रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-20}{4}=5\). Keep the sign of (b) correct in the formula.
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If the roots of \(x^2+mx+30=0\) are (-5) and (-6), what is the value of (m)?
A. (11)
मूलों का योग (-11) है और (-m=-11) होगा। इसलिए (m=11) है। / The sum of roots is (-11), and (-m=-11). Therefore (m=11).
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What is the sum of roots of \(6x^2-13x+5=0\)?
A. \(\frac{13}{6}\)
मूलों का योग \(-\frac{b}{a}\) होता है। यहां (a=6) और (b=-13) हैं इसलिए योग \(\frac{13}{6}\) है। / The sum of roots is \(-\frac{b}{a}\). Here (a=6) and (b=-13), so the sum is \(\frac{13}{6}\).
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If \(\alpha\) and \(\beta\) are roots of \(3x^2-12x+5=0\), what is \(\alpha+\beta\)?
A. (4)
मूलों का योग \(-\frac{b}{a}=-\frac{-12}{3}=4\) है। सूत्र में (b) का चिन्ह सही रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-12}{3}=4\). Keep the sign of (b) correct in the formula.
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If the roots of \(x^2+mx+20=0\) are (-4) and (-5), what is the value of (m)?
A. (9)
मूलों का योग (-9) है और (-m=-9) होगा। इसलिए (m=9) है। / The sum of roots is (-9), and (-m=-9). Therefore (m=9).
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What is the sum of roots of \(4x^2-11x+7=0\)?
A. \(\frac{11}{4}\)
मूलों का योग \(-\frac{b}{a}\) होता है। यहां (a=4) और (b=-11) इसलिए योग \(\frac{11}{4}\) है। / The sum of roots is \(-\frac{b}{a}\). Here (a=4) and (b=-11), so the sum is \(\frac{11}{4}\).
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If \(\alpha\) and \(\beta\) are roots of \(2x^2-6x+1=0\), what is \(\alpha+\beta\)?
A. (3)
मूलों का योग \(-\frac{b}{a}=-\frac{-6}{2}=3\) है। सूत्र में (b) का चिन्ह सही रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-6}{2}=3\). Keep the sign of (b) correct in the formula.
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If the roots of \(x^2+mx+12=0\) are (-3) and (-4), what is the value of (m)?
A. (7)
मूलों का योग (-7) है और (-m=-7) होगा। इसलिए (m=7) है। / The sum of roots is (-7), and (-m=-7). Therefore (m=7).
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What is the sum of roots of \(5x^2-4x-1=0\)?
A. \(\frac{4}{5}\)
मूलों का योग \(-\frac{b}{a}\) होता है। यहां (a=5) और (b=-4) इसलिए योग \(\frac{4}{5}\) है। / The sum of roots is \(-\frac{b}{a}\). Here (a=5) and (b=-4), so the sum is \(\frac{4}{5}\).
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What is the sum of roots of \(x^2-13x+42=0\)?
A. (13)
मूलों का योग \(-\frac{b}{a}\) है। यहां (b=-13) इसलिए योग (13) है। / The sum of roots is \(-\frac{b}{a}\). Here (b=-13), so the sum is (13).
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What is the sum of roots of \(2x^2+3x-5=0\)?
A. \(-\frac{3}{2}\)
मूलों का योग \(-\frac{b}{a}\) होता है। यहां योग \(-\frac{3}{2}\) है। / The sum of roots is \(-\frac{b}{a}\). Here the sum is \(-\frac{3}{2}\).
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What is the sum of roots of \(x^2+11x+30=0\)?
B. (-11)
मूलों का योग \(-\frac{b}{a}\) है। यहां योग (-11) होगा। / The sum of roots is \(-\frac{b}{a}\). Here the sum is (-11).
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What is the sum of roots of \(3x^2-5x+2=0\)?
A. \(\frac{5}{3}\)
मूलों का योग \(-\frac{b}{a}\) होता है। यहां (a=3) और (b=-5) इसलिए योग \(\frac{5}{3}\) है। / The sum of roots is \(-\frac{b}{a}\). Here (a=3) and (b=-5), so the sum is \(\frac{5}{3}\).
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What is the sum of roots of \(x^2+7x+10=0\)?
C. (-7)
मूलों का योग \(-\frac{b}{a}\) है इसलिए यहां (-7) होगा। गुणनखंड न बनाकर भी यह जल्दी निकलता है। / The sum of roots is \(-\frac{b}{a}\) so here it is (-7). This can be found quickly without factorising.
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If \(\alpha\) and \(\beta\) are roots of \(ax^2+bx+c=0\) then what is \(\alpha+\beta\)?
A. \(-\frac{b}{a}\)
द्विघात समीकरण में मूलों का योग \(-\frac{b}{a}\) होता है। सूत्र लगाते समय (b) का चिन्ह सही रखें। / For a quadratic equation the sum of roots is \(-\frac{b}{a}\). Keep the sign of (b) correct while using the formula.
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Which equation will have sum of roots (0)?
A. \(x^2-36=0\)
\(x^2-36=0\) में (b=0), इसलिए मूलों का योग \(-\frac{b}{a}=0\) है। (x) पद अनुपस्थित हो तो योग (0) हो सकता है। / In \(x^2-36=0\), (b=0), so the sum of roots is \(-\frac{b}{a}=0\). If the (x) term is absent, the sum can be (0).
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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 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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If the sum of roots of \(3x^2+nx+12=0\) is (-4), what is (n)?
A. (12)
मूलों का योग \(-\frac{n}{3}=-4\), इसलिए (n=12) है। योग के सूत्र में ऋण चिन्ह न भूलें। / The sum of roots is \(-\frac{n}{3}=-4\), so (n=12). Do not forget the negative sign in the sum formula.
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What is the sum of roots of \(4x^2-7x+2=0\)?
A. \(\frac{7}{4}\)
मूलों का योग \(-\frac{b}{a}=-\frac{-7}{4}=\frac{7}{4}\) है। सूत्र में (b) का चिन्ह ध्यान से रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-7}{4}=\frac{7}{4}\). Pay attention to the sign of (b) in the formula.
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If the sum of roots of \(2x^2+mx+8=0\) is (-3), what is (m)?
A. (6)
मूलों का योग \(-\frac{m}{2}=-3\), इसलिए (m=6) है। योग के सूत्र में ऋण चिन्ह पर ध्यान दें। / The sum of roots is \(-\frac{m}{2}=-3\), so (m=6). Notice the negative sign in the sum formula.
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What is the sum of roots of \(2x^2-5x+3=0\)?
A. \(\frac{5}{2}\)
मूलों का योग \(-\frac{b}{a}=-\frac{-5}{2}=\frac{5}{2}\) है। सूत्र में (b) का चिन्ह ध्यान से रखें। / The sum of roots is \(-\frac{b}{a}=-\frac{-5}{2}=\frac{5}{2}\). Pay attention to the sign of (b) in the formula.
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Which option makes \(\sqrt{a}+\sqrt{b}\) irrational?
C. (a=4,b=18)
(a=4) पर \(\sqrt{4}=2\) है। / For (a=4), \(\sqrt{4}=2\).
(b=18) पर \(\sqrt{18}=3\sqrt{2}\), जो अपरिमेय है; इसलिए योग \(2+3\sqrt{2}\) अपरिमेय है। / For (b=18), \(\sqrt{18}=3\sqrt{2}\), which is irrational; so the sum \(2+3\sqrt{2}\) is irrational.
यदि एक पद परिमेय और दूसरा अपरिमेय हो, तो योग अपरिमेय रहता है। / A rational plus an irrational remains irrational.
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In which option is \(\sqrt{a}+\sqrt{b}\) definitely rational?
B. (a=9,b=16)
\(\sqrt{9}=3\) और \(\sqrt{16}=4\) हैं। / \(\sqrt{9}=3\) and \(\sqrt{16}=4\).
इनका योग (7) परिमेय है। / Their sum is (7), which is rational.
दोनों मूल यदि पूर्ण वर्गों के हों, तो योग आसानी से परिमेय बनता है। / If both radicands are perfect squares, the sum is easily rational.
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