Which of the following equations is quadratic in form?

• A. $x^3-2x+1=0$
• B. $3x+7=0$
• C. $\frac{4}{x}-1=0$
• D. $x^2+5x-6=0$

Answer: (D)

Verified step by step guidance

1. Recall that a quadratic equation is any equation that can be written in the form \(a x^{2} + b x + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
2. Examine each given equation to identify the highest power of \(x\) and see if it matches the quadratic form:
3. 1. \(x^{3} - 2x + 1 = 0\) has the highest power of \(x\) as 3, so it is cubic, not quadratic.
4. 2. \$3x + 7 = 0\( has the highest power of \)x$ as 1, so it is linear, not quadratic.
5. 3. \(\frac{4}{x} - 1 = 0\) involves \(x\) in the denominator, which is not a polynomial form, so it is not quadratic.
6. 4. \(x^{2} + 5x - 6 = 0\) has the highest power of \(x\) as 2 and fits the form \(a x^{2} + b x + c = 0\), so this is quadratic.