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allsm [11]
3 years ago
12

Joline is solving the equation 0 = x2 – 5x – 4 using the quadratic formula. Which value is the negative real number solution to

her quadratic equation? Round to the nearest tenth if necessary. Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction –5.7 –4 –1 –0.7
Mathematics
1 answer:
katen-ka-za [31]3 years ago
4 0

Answer:

- 0.7

Step-by-step explanation:

We are given the general quadratic formula, as " x = -b \frac{+}{-}  \sqrt{(b^2-4ac)} / 2a. " This can be represented by two separate formula's, which will come in handy when determining the positive and negative roots of the equation ( and here we need the negative root ):

1 ) x = - b+ ( \sqrt{b^2-4ac} ) / 2a,

2 ) x = - b- ( \sqrt{b^2-4ac} ) / 2a

We know that a = 1, b = - 5, and c = - 4 from the equation " 0 = x^2 - 5x - 4 " ( which can be rewritten in the form 0 = ax^2 + bx + c ). Therefore, simply plug in these values into the quadratic formula to receive two solutions:

x = 5 + ( \sqrt{( - 5 )^2 - 4( 1 )( - 4 )} ) / 2( 1 ),\\x = 5 + ( \sqrt{25 + 16} ) / 2,\\x = 5 + \sqrt{41} / 2,\\x = ( About ) 5.7- This is our positive solution

__________

x = 5 - ( \sqrt{( - 5 )^2 - 4( 1 )( - 4 )} ) / 2( 1 ),\\x = 5 - ( \sqrt{25 + 16} ) / 2,\\x = 5 - \sqrt{41} / 2,\\x = ( About ) - 0.7- And this is our negative solution

You can see that - 0.7 is the negative real number solution to Joline's quadratic equation!

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Step-by-step explanation:

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Comment on factoring

When the leading coefficient is 1, the coefficient of the x-term is the sum of the constants in the binomial factors, and the constant term is their product. You can see this by multiplying out the generic case:

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