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(D) The minimum value of a quadratic expression $ax^2 + bx + c$ (where $a > 0$) is given by the formula $\frac{4ac - b^2}{4a}$.$i) x^2 + 4x + 6$: Here

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$i)$ $\rightarrow b, ii)$ $\rightarrow c, iii)$ $\rightarrow d, iv)$ $\rightarrow a$

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(D) The minimum value of a quadratic expression $ax^2 + bx + c$ (where $a > 0$) is given by the formula $\frac{4ac - b^2}{4a}$.$i) x^2 + 4x + 6$: Here $a=1, b=4, c=6$. Minimum value = $\frac{4(1)(6) - (4)^2}{4(1)} = \frac{24 - 16}{4} = \frac{8}{4} = 2$. So,$i \rightarrow b$.$ii) x^2 - 2x + 5$: Here $a=1, b=-2, c=5$. Minimum value = $\frac{4(1)(5) - (-2)^2}{4(1)} = \frac{20 - 4}{4} = \frac{16}{4} = 4$. So,$ii \rightarrow c$.$iii) x^2 + 6x + 18$: Here $a=1, b=6, c=18$. Minimum value = $\frac{4(1)(18) - (6)^2}{4(1)} = \frac{72 - 36}{4} = \frac{36}{4} = 9$. So,$iii \rightarrow d$.$iv) x^2 - 4x + 5$: Here $a=1, b=-4, c=5$. Minimum value = $\frac{4(1)(5) - (-4)^2}{4(1)} = \frac{20 - 16}{4} = \frac{4}{4} = 1$. So,$iv \rightarrow a$.Thus,the correct matching is $i$ $\rightarrow b, ii$ $\rightarrow c, iii$ $\rightarrow d, iv$ $\rightarrow a$.

Quadratic expression	The minimum value
i) $x^2 + 4x + 6$	a) $1$
ii) $x^2 - 2x + 5$	b) $2$
iii) $x^2 + 6x + 18$	c) $4$
iv) $x^2 - 4x + 5$	d) $9$

Column-$I$	Column-$II$
$A$. Imaginary roots	$P$. $a \in (-1, 4)$
$B$. One root less than $3$ and other greater than $3$	$Q$. $a \in (-\infty, -1)$
$C$. One root less than $1$ and other greater than $3$	$R$. $a \in (-\infty, -4/3)$

Match the following quadratic expressions with their minimum values:
Quadratic expression The minimum value
i) $x^2 + 4x + 6$ a) $1$
ii) $x^2 - 2x + 5$ b) $2$
iii) $x^2 + 6x + 18$ c) $4$
iv) $x^2 - 4x + 5$ d) $9$

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Match the following quadratic expressions with their minimum values:Quadratic expressionThe minimum valuei) $x^2 + 4x + 6$a) $1$ii) $x^2 - 2x + 5$b) $2$iii) $x^2 + 6x + 18$c) $4$iv) $x^2 - 4x + 5$d) $9$