Paragraph: Let a x^3+b x^2+c x+d=| array lcc x+1 & 2 x & 3 x 2 x+3 & x+1 & x 2-x & 3 x+4 & 5 x-1 array | then Question: What is the value of c ?

Correct answer: C. 35 aligned & ax^3+bx^2+cx+d & aligned =(x+1)[(x+1)(5 x-1)-x(3 x+4)]-2 x[(2 x+3)(5 x-1) -x(2-x)]+3 x[(2 x+3)(3 x+4)-(2-x)(x+1)] aligned aligned aligned & a x^3+b x^2+c x+d=x^3+28 x^2+35 x-1 & c=35 aligned

NDA 2016

Exam: NDA
Year: 2016
Subject: Mathematics
Chapter: Determinants

NDA 2016 · Mathematics · Determinants

Paragraph: Let a x^3+b x^2+c x+d=| array lcc x+1 & 2 x & 3 x 2 x+3...

Paragraph: Let

a x^3+b x^2+c x+d=\left|

\begin{array}{lcc}x+1 & 2 x & 3 x \\ 2 x+3 & x+1 & x \\ 2-x & 3 x+4 & 5 x-1\end{array}

\right|

thenQuestion: What is the value of

c

Options

A $-1$
B $34$
C $35$
D $50$

Correct answer

C. $35$

Step-by-step solution

\begin{aligned} & \mathrm{ax}^3+\mathrm{bx}^2+\mathrm{cx}+\mathrm{d} \\ & \begin{aligned}=(\mathrm{x}+1)[(x+1)(5 x-1)-\mathrm{x}(3 \mathrm{x}+4)]-2 \mathrm{x}[(2 \mathrm{x}+3)(5 \mathrm{x}-1) \\ \quad-\mathrm{x}(2-\mathrm{x})]+3 \mathrm{x}[(2 \mathrm{x}+3)(3 x+4)-(2-x)(x+1)]\end{aligned}

\end{aligned}

\begin{aligned} & \Rightarrow \quad a x^3+b x^2+c x+d=x^3+28 x^2+35 x-1 \\ & \Rightarrow \quad c=35\end{aligned}

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