Solving the Quadratic Equation
The given equation is a quadratic equation:
\(12x^2 + 45x = 0\)
To solve for x, we can factor out the common term, which is x.
Factorization Step
Factor out x from the equation:
\(x(12x + 45) = 0\)
Applying the Zero Product Property
According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.
This gives us two possible cases:
- Case 1: The first factor is zero. \(x = 0\)
- Case 2: The second factor is zero. \(12x + 45 = 0\)
Solving for x in Case 2
Solve the linear equation from Case 2:
- Subtract 45 from both sides: \(12x = -45\)
- Divide both sides by 12: \(x = \frac{-45}{12}\)
- Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3: \(x = \frac{-45 \div 3}{12 \div 3} = \frac{-15}{4}\)
Final Solutions
The solutions for the equation \(12x^2 + 45x = 0\) are:
\(x = 0 \quad \text{and} \quad x = \frac{-15}{4}\)
Similar Questions
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Important Questions from Quadratic equation
Find the minimum value of 2x² – 5x – 3 and also find x.
A quadratic equation $x^2 + 3x + k = 0$ has a discriminant equal to 9. What is the value of k?
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If both roots of the quadratic equation, $x^2 + 3x + 2 = 0$, are also roots of another quadratic equation, $ax^2 + bx + c = 0$, then which of the following must be true?
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