Understanding Quadratic Equations
A quadratic equation is a polynomial equation where the highest power (degree) of the variable is 2. The standard form is \(ax^2 + bx + c = 0\), where \(a \neq 0\). We need to find the option where the variable '\(x\)' has a maximum exponent of 2.
Analyzing the Options
Let's examine each option to determine the highest power of '\(x\)':
- Option 1: \(x^2+3x^3+5\)
The highest power of '\(x\)' is 3 (from the term \(3x^3\)). This is a cubic equation, not quadratic.
- Option 2: \(x^{3/5}+y^2-3\)
This equation contains a fractional exponent (\(x^{3/5}\)). Quadratic equations must have integer exponents, specifically a highest exponent of 2.
- Option 3: \(5x^2+4-7x\)
The terms are \(5x^2\), $4$ (which is \(4x^0\)), and \(-7x\) (which is \(-7x^1\)). The highest power of '\(x\)' is 2. This equation can be written in standard form as \(5x^2 - 7x + 4 = 0\). Therefore, this is a quadratic equation.
- Option 4: \(x^2-2x^{1/5}+2\)
This equation includes a fractional exponent (\(x^{1/5}\)), disqualifying it as a quadratic equation.
- Option 5:
This option is empty and cannot be evaluated.
Identifying the Quadratic Equation
Based on the analysis, the only equation that meets the definition of a quadratic equation (highest power of \(x\) is 2) is Option 3.
Similar Questions
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- Find the zeros of the function \(f(x) = (x - 17)(x - 7)\)
- Find the roots of the following equation
$x^2 + 12x - 36 = 0$ - Which of the following equations are quadratic equations?
I) $x^2 + 4x + 23 = x + \frac{33}{28}$
II) $\frac{2}{3}x^2 + 6x + 2 = x^2 + 8$
III) $6x^2 + 4x + 18 = 6x^2 - 6x$ - Find the roots of the following equation:
$4x^2 + 4x - 3 = 0$ - Sum of the zeros of the equation \(3x^2+2x-5\) is?
- Zeros of the equations \(x^2-7x+6=0\) are
- If $12x^2 - ax + 7 = ax^2 + 9x + 3$ has only one (repeated) solution, then the positive integral solution of $a$ is:
If (x - 1) 2+ (y - 2) 2= (x – 1) (y - 2), where x and y are integers, then value of 2x + 3y is:
- Zeros of equation \(x^2-9x+18=0\) are
Important Questions from Quadratic Equations
If the graph of a quadratic polynomial lies entirely above x-axis, then which one of the following is correct?
If the roots of the equation x 2+ px + q = 0 are tan 19° and tan 26°, then which one of the following is correct?
If x 2- px + 4 > 0 for all real values of x, then which one of the following is correct?
If 2 + i is a root of the equation x 2- ax + 1 = 0, then the value of a is:
If \(\tan \left( {\frac{α }{2}} \right)\) and \(\tan \left( {\frac{β }{2}} \right)\) are the roots of the equation 8x 2- 26x + 15 = 0, then the value of cos (α + β) will be
