If p - 0 solution set of the equation - -1 1 x p-1 p-1 p-x 3 x-1 x-2-0 is

The correct option is A { 1,2 } Applying C_2→ C_2 C_1 we get 1 amp;0 nbsp; amp;x nbsp;p+1 amp; 0 amp; p+x nbsp;3 ...

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Byju's Answer

Standard XII

Chemistry

Gibb's Energy and Nernst Equation

If p ≠ 0 so...

Question

If $p \neq 0$ solution set of the equation
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & x p + 1 & p + 1 & p + x 3 & x + 1 & x + 2 \end{matrix} ∣ ∣ ∣ ∣ = 0$ is

{1, 2}

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{2, 3}

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{1, p, 2}

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{1, 2, - p}

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Solution

The correct option is A ${1, 2}$
$A p p l y i n g C_{2} \to C_{2} - C_{1}$ we get
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & x p + 1 & 0 & p + x 3 & x - 2 & x + 2 \end{matrix} ∣ ∣ ∣ ∣ = - (x - 2) ∣ ∣ ∣ \begin{matrix} 1 & x p + 1 & p + x \end{matrix} ∣ ∣ ∣$
$= (x - 2) ∣ ∣ ∣ \begin{matrix} 1 & x p & p \end{matrix} ∣ ∣ ∣ = (x - 2) p (1 - x) = 0$
$\Rightarrow$ Thus $Δ = 0, x = 1, 2$

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If p≠0 solution set of the equationΔ=∣∣ ∣∣11xp+1p+1p+x3x+1x+2∣∣ ∣∣=0 is

The correct option is A {1,2}Applying C2→C2−C1 we get∣∣ ∣∣10xp+10p+x3x−2x+2∣∣ ∣∣=−(x−2)∣∣∣1xp+1p+x∣∣∣=(x−2)∣∣∣1xpp∣∣∣=(x−2)p(1−x)=0⇒ Thus Δ=0,x=1,2

If $p \neq 0$ solution set of the equation
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & x p + 1 & p + 1 & p + x 3 & x + 1 & x + 2 \end{matrix} ∣ ∣ ∣ ∣ = 0$ is