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Quadratic Formula

If 3x4-27x3...

Question

If $3 x^{4} - 27 x^{3} + 36 x^{2} - 5 = 0$ , then $s_{1} + s_{2}$ , where $s_{i}$ denotes sum of roots taken $i$ at a time, is

3

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21

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Solution

The correct option is B $21$
Given equation is $3 x^{4} - 27 x^{3} + 36 x^{2} - 5 = 0$
Comparing with the standard form $a x^{3} + b x^{2} + x c + d = 0$ , we get
$a = 3, b = - 27, c = 36, d = - 5$

$S_{1} = α + β + γ = - \frac{b}{a}$ and $S_{2} = α β + α γ + β γ = \frac{c}{a}$

$S_{1} = - (- \frac{27}{3}) = 9 S_{2} = \frac{36}{3} = 12$

Therefore, $S_{1} + S_{2} = 9 + 12 = 21$

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If 3x4−27x3+36x2−5=0, then s1+s2, where si denotes sum of roots taken i at a time, is

The correct option is B 21Given equation is 3x4−27x3+36x2−5=0Comparing with the standard form ax3+bx2+xc+d=0, we geta=3,b=−27,c=36,d=−5S1=α+β+γ=−ba and S2=αβ+αγ+βγ=caS1=−(−273)=9S2=363=12Therefore, S1+S2=9+12=21

If $3 x^{4} - 27 x^{3} + 36 x^{2} - 5 = 0$ , then $s_{1} + s_{2}$ , where $s_{i}$ denotes sum of roots taken $i$ at a time, is