Solve. x + 3 5 = 2 A) -5 B) -3 Eliminate C) 7 D) 13
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Answer:
In general, quadratic equations have two x-intercepts. But sometimes it happens that a quadratic eqution has one x-intercept or no interepts. That's why we should fully analyze this equation:
Given the following equation: y=3x^2 + 7 + m
If y=0, then:
3x^2 + 7 + m = 0 ⇒ x^2 = (-m-7)/3
Then ±
Given that we can take the square root of a negative number, the only way this equation has two x-intercepts is if m<-7.
Summarizing:
The equation: y=3x^2 + 7 + m has two x-intercepts only if m is less than -7. If m equals -7, the equation has only one x-intercept, and finally, if m is greater than -7, the equation has NO x-intercepts.