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Chapter 2: Problem 99

Is it possible for a quadratic equation to have only one \(x\) -intercept? Explain.

Short Answer

Expert verified
Yes, it is possible for a quadratic equation to have only one x-intercept. This happens when the discriminant of the equation is equal to 0.

Step by step solution

01

Understand the characteristics of the quadratic equation

A quadratic equation may have zero, one, or two x-intercepts. This usually depends on the value of the discriminant, which is calculated as \(D = b^{2} - 4ac\).
02

Calculate the discriminant

If the discriminant \(D = b^{2} - 4ac\) equals zero, then the quadratic equation has exactly one x-intercept. This is because the equation relies on the square root of the discriminant, and the square root of zero is zero. This results in one solution, typically referred to as a repeated root.
03

Final conclusion

So, to conclude, yes, it is possible for a quadratic equation to have only one x-intercept. This occurs when the discriminant of the equation equals zero.

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Most popular questions from this chapter

Write a rational function \(f\) that has the specified characteristics. (There are many correct answers.) (a) Vertical asymptote: \(x=2\) Horizontal asymptote: \(y=0\) Zero: \(x=1\) (b) Vertical asymptote: \(x=-1\) Horizontal asymptote: \(y=0\) Zero: \(x=2\) (c) Vertical asymptotes: \(x=-2, x=1\) Horizontal asymptote: \(y=2\) Zeros: \(x=3, x=-3\), (d) Vertical asymptotes: \(x=-1, x=2\) Horizontal asymptote: \(y=-2\) Zeros: \(x=-2, x=3\)

Solve the inequality and write the solution set in interval notation. \(x^{4}(x-3) \leq 0\)

Solve the inequality and graph the solution on the real number line. \(x^{2} \leq 16\)

Solve the inequality and graph the solution on the real number line. \(x^{2}-6 x+9<16\)

The formula that relates cost, revenue, and profit is _____________.
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