10.Solving Quadratic Equations

Passport to advanced mathematics Part I solving quadratic equations

1. Which of the following could be the factored form of the polynomial shown below? −18  x 2+3 x −18 A.  x  −3! x  +"!  x −3!  x +"! #.  x  +3! x  −"!  x +3!  x −"! $.  x  −3! x  −"!  x −3!  x −"! %.  x  +3! x  +"!  x +3!  x +"! $orr orrect ect answ answer er&& A di'cu i'cult lt degr egree& ee& 1 2. Which of the following could be the factored form of the polynomial shown below? +"(  x 2+1" x +"( A.  x  +"! x  +1(!  x +"!  x +1(! #.  x  +"! x  −1(!  x +"!  x −1(! $.  x  −"! x  +1(!  x −"!  x +1(! %.  x   x −"! −"! x   x −1(! −1(! $orr orrect ect answ answer er&& A di'cu i'cult lt degr egree& ee& 1 3. Which of the following could be the factored form of the polynomial shown below? +2)  x 2+12 x +2) A.  x  −3!  x  +*!  x −3!  x +*! #.  x   x +3! +3!  x   x −*! −*! $.  x   x −3! −3!  x   x −*! −*! %.  x   x +3! +3!  x   x +*! +*! $orrect $orrect answer& %di'cult % di'cult degree& 1 . Which of the following could be the factored form of the polynomial shown below? −"  x 2− x −" A.  x   x −3! −3!  x   x +2! +2! #.  x   x +3! +3!  x   x +2! +2! $.  x  −3!  x  −2!  x −3!  x −2! %.  x  +3!  x  −2!  x +3!  x −2! $orr orrect ect answ answer er&& A di'cu i'cult lt degr egree& ee& 1 ,. Which of the following could be the factored form of the polynomial shown below?  x 2+3 x −28 −28 A.  x   x +)! +)!  x   x −! −! #.  x  −)!  x  −!  x −)!  x −!

$.  x  +)!  x  +!  x +)!  x +! %.  x  −)!  x  +!  x −)!  x +! $orr orrect ect answ answer er&& A

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". 1(( ((−1 −12 21k 2-( What are the solutions to the euation abo/e? A. 0-

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). 2 x −3! −3! x   x +!-( +!-( et  x -a and x -b be the solutions to the euation abo/e. What is the /alue of − a−b? $orrect $orrect answer& ,2 di'cult degree& 2 8. (-2 y −1!8− −1!8− y ! et y -u and y -d be the solutions to the euation abo/e. What is the /alue of  u  ud? $orrect answer&  di'cult degree& 2 *. 2 x +,!− +,!−mx +*!-( +*!-( 4n the euati euation on abo/e5 abo/e5 m is a cons consta tant nt.. 4f the the eua euati tion on has has the the 5

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6ow many distinct real solutions does the euation abo/e ha/e? A. ( #. 1 $. 2 %.  $orr orrect ect answ answer er&& $ di'cu i'cult lt degr egree& ee& 2

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et 7-w and 7- be the solutions to the euation abo/e. What is the /alue of w+? 3

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What are the solutions to the euation abo/e? A. 7- − #. 7- −

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13.t +1,! +1,!2+,-( 6ow many distinct real solutions does the euation abo/e ha/e? A. ( #. 1 $. 2 %.  $orr orrect ect answ answer er&& A di'cu i'cult lt degr egree& ee& 3 1. x 2−13 x +3(-( +3(-( What are the solutions to the euation abo/e? A. 77-−1 −1, , and and 77-2 2 #. 77-−1( −1( and and 7-: 7-:3 3 $. 7 - 3 and and 77-1( 1( %. 77-:2 :2 and and 7-1 7-1, , $orr orrect ect answ answer er&& $ di'cu i'cult lt degr egree& ee& 3 1,.2 x 2+, x −k -( -( 4n the euation abo/e5 k  is  is a constant. ;or what /alue of k  does   does the euation ha/e e7actly one distinct real solution? A.

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1".t −1(! −1(!2−1"-( What are the solutions to the euation abo/e? A. t- t- and and t-3" t-3" #. t-" t-" and and t-1 t-1 $. t-1( t-1( and and t-−1 t-−1" " %. t-1( t-1( and and t-1 t-1" " $orr orrect ect answ answer er&& # di'cu i'cult lt degr egree& ee& 3 1). x −1-2− −1-2− x !2 What are the solutions to the euation abo/e? A. 7-( 5 − √ 5 5 + √ 5 #. 7 and 72

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