单选题By how much does the sum of the roots of the equation (x+1) (x-3) = 0 exceed the product of its roots?A1B2C3D4E5
单选题
By how much does the sum of the roots of the equation (x+1) (x-3) = 0 exceed the product of its roots?
A
1
B
2
C
3
D
4
E
5
参考解析
解析：
If (x+1)(x-3)=0, then x+1=0 or x-3 = 0. Hence, x = -1 or x = 3. The sum of these roots is -1+3 or 2, and their product is (-1)×(3) = -3. Since 2-(-3)=2+3=5 the sum of the roots of the equation exceeds the product of its roots by 5.
If (x+1)(x-3)=0, then x+1=0 or x-3 = 0. Hence, x = -1 or x = 3. The sum of these roots is -1+3 or 2, and their product is (-1)×(3) = -3. Since 2-(-3)=2+3=5 the sum of the roots of the equation exceeds the product of its roots by 5.
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