Quadratic Equations Warmup

Algebra Level 1

If ( x + 4 ) ( 3 x − 1 ) = a x 2 + b x + c , (x + 4)(3x - 1) = ax^2 + bx + c, what is the value of a + b + c ? a + b + c?

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2 solutions

Given that:

a x 2 + b x + c = ( x + 4 ) ( 3 x − 1 ) Putting x = 1 a + b + c = ( 1 + 4 ) ( 3 − 1 ) = 10 \begin{aligned} ax^2 + bx + c & = (x+4)(3x-1) & \small \blue{\text{Putting }x=1} \\ a + b + c & = (1+4)(3-1) = \boxed{10} \end{aligned}

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@Chew-Seong Cheong - How do you put that big space between the black text and blue text, sir?

A Former Brilliant Member - 10 months, 2 weeks ago

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Hope that this help. "&" is used to align. The first "&" to left-align the "=" sign and the second "&" is to right-align the blue text. You can add more blue text in other lines and they will be aligned,

Chew-Seong Cheong - 10 months, 1 week ago

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Thank you @Chew-Seong Cheong !

A Former Brilliant Member - 10 months, 1 week ago
Brilliant Mathematics Staff
Aug 1, 2020

When we multiply the factors together, we get:

( x + 4 ) ( 3 x − 1 ) = 3 x 2 + 12 x − 1 x − 4 = 3 x 2 + 11 x − 4 (x + 4)(3x -1) = 3x^2 + 12x - 1x - 4 = 3x^2 + 11x - 4

a = 3 , b = 11 , c = − 4 a = 3, b = 11, c = -4

a + b + c = 3 + 11 + ( − 4 ) = 10 a + b + c = 3 + 11 + (-4) = 10

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