Use the Quadratic Formula to solve 12 x 2 − 12 x + 3 = 0 12 x ^ { 2 } - 12 x + 3 = 0 12 x 2 − 12 x + 3 = 0 .A) x = 1 2 x = \frac { 1 } { 2 } x = 2 1 B) x = 1 2 ± 12 2 x = \frac { 1 } { 2 } \pm 12 \sqrt { 2 } x = 2 1 ± 12 2 C) x = 12 2 x = 12 \sqrt { 2 } x = 12 2 D) x = − 1 2 x = - \frac { 1 } { 2 } x = − 2 1 E) no solutions

Question

Use the Quadratic Formula to solve   12 x 2 − 12 x + 3 = 0 12 x ^ { 2 } - 12 x + 3 = 0 12 x 2 − 12 x + 3 = 0   .A)    x = 1 2 x = \frac { 1 } { 2 } x = 2 1 ​ B)    x = 1 2 ± 12 2 x = \frac { 1 } { 2 } \pm 12 \sqrt { 2 } x = 2 1 ​ ± 12 2 ​ C)    x = 12 2 x = 12 \sqrt { 2 } x = 12 2 ​ D)    x = − 1 2 x = - \frac { 1 } { 2 } x = − 2 1 ​ E) no solutions

Adhari Alnuamee · Accepted Answer

Final Answer : A, Explanation :   The quadratic formula is   x = − b ± b 2 − 4 a c 2 a x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} x = 2 a − b ± b 2 − 4 a c ​ ​  , where   a = 12 a = 12 a = 12  ,   b = − 12 b = -12 b = − 12  , and   c = 3 c = 3 c = 3  . Plugging these values in, we get   x = 12 ± ( − 12 ) 2 − 4 ( 12 ) ( 3 ) 2 ( 12 ) = 12 ± 144 − 144 24 = 12 ± 0 24 = 1 2 x = \frac{12 \pm \sqrt{(-12)^2 - 4(12)(3)}}{2(12)} = \frac{12 \pm \sqrt{144 - 144}}{24} = \frac{12 \pm 0}{24} = \frac{1}{2} x = 2 ( 12 ) 12 ± ( − 12 ) 2 − 4 ( 12 ) ( 3 ) ​ ​ = 24 12 ± 144 − 144 ​ ​ = 24 12 ± 0 ​ = 2 1 ​  .

Use the Quadratic Formula to solve $12 x ^ { 2 } - 12 x + 3 = 0$ .

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 2 } \pm 12 \sqrt { 2 }$
C) $\sqrt { 2 }$
D) $\frac { 1 } { 2 }$
E) no solutions

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Use the Quadratic Formula to solve 12x2−12x+3=012 x ^ { 2 } - 12 x + 3 = 012x2−12x+3=0 .A) x=12x = \frac { 1 } { 2 }x=21​ B) x=12±122x = \frac { 1 } { 2 } \pm 12 \sqrt { 2 }x=21​±122​ C) x=122x = 12 \sqrt { 2 }x=122​ D) x=−12x = - \frac { 1 } { 2 }x=−21​ E) no solutions

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Learning Objectives

Learning Objectives

Related questions

Use the Quadratic Formula to solve $12 x ^ { 2 } - 12 x + 3 = 0$ .

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 2 } \pm 12 \sqrt { 2 }$
C) $\sqrt { 2 }$
D) $\frac { 1 } { 2 }$
E) no solutions