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(A) The discriminant $D$ of a quadratic equation $ax^{2}+bx+c=0$ is given by $D = b^{2}-4ac$.$1.$ For $x^{2}+5x+6=0$,$D = 5^{2}-4(1)(6) = 25-24 = 1$.

Vedclass · Accepted Answer

$(1-d), (2-c), (3-b), (4-a)$

Vedclass · Answer

(A) The discriminant $D$ of a quadratic equation $ax^{2}+bx+c=0$ is given by $D = b^{2}-4ac$.$1.$ For $x^{2}+5x+6=0$,$D = 5^{2}-4(1)(6) = 25-24 = 1$. Thus,$(1-a)$.$2.$ For $x^{2}+5x+4=0$,$D = 5^{2}-4(1)(4) = 25-16 = 9$. Thus,$(2-b)$.$3.$ For $x^{2}+4x+3=0$,$D = 4^{2}-4(1)(3) = 16-12 = 4$. Thus,$(3-c)$.$4.$ For $x^{2}+6x+5=0$,$D = 6^{2}-4(1)(5) = 36-20 = 16$. Thus,$(4-d)$.Matching these,we get $(1-a), (2-b), (3-c), (4-d)$. Note: The provided options in the prompt were inconsistent with the calculation; based on the standard calculation,the correct match is $(1-a), (2-b), (3-c), (4-d)$.

Part $I$	Part $II$
$1.$ The discriminant of $x^{2}+5x+6=0$	$a. 1$
$2.$ The discriminant of $x^{2}+5x+4=0$	$b. 9$
$3.$ The discriminant of $x^{2}+4x+3=0$	$c. 4$
$4.$ The discriminant of $x^{2}+6x+5=0$	$d. 16$

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