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Subject Test Math 1

Question 6 of 32

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SAT Subject Test

The sum of the two roots of a quadratic equation is 5 and their product is negative 6. Which of the following could be the equation?

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x squared invisible times minus text   end text 6 x invisible times plus text   end text 5 invisible times equals text   end text 0

Correct Answer: 
No

x squared invisible times minus text   end text 5 x invisible times minus text   end text 6 invisible times equals text   end text 0

Correct Answer: 
Yes

x squared invisible times minus text   end text 5 x invisible times plus text   end text 6 invisible times equals text   end text 0

Correct Answer: 
No

x squared invisible times text   end text plus text   end text 5 x invisible times minus text   end text 6 invisible times equals text   end text 0

Correct Answer: 
No

x squared invisible times plus text   end text 6 x invisible times plus text   end text 5 invisible times equals text   end text 0

Correct Answer: 
No

One way to do this problem is to think about the properties of roots. Suppose the two roots of a quadratic equation are a and b. Then the quadratic equation can be written in factored form as left parenthesis x invisible times minus a right parenthesis left parenthesis x invisible times minus b right parenthesis invisible times equals 0. The sum of the roots is a invisible times plus b, and the product is a b.

Note thatleft parenthesis x minus a right parenthesis left parenthesis x invisible times minus b right parenthesis equals x to the power of 2 end exponent invisible times minus left parenthesis a invisible times plus b right parenthesis x invisible times plus a b. In this question the sum of the roots is 5 and the product is negative 6. Therefore, left parenthesis a invisible times plus b right parenthesis equals 5 and a b invisible times equals negative 6. The equation could be x to the power of 2 end exponent invisible times minus 5 x invisible times minus 6 invisible times equals 0, which is choice B. Note that the roots of this equation are 6 and negative 1. Their sum is 5 and their product is negative 6.

If you know these properties of roots, you do not need to factor all of the equations to find the one that fits the given conditions.

Question Difficulty: 
medium