Question
Zeros of equation \(x^2-9x+18=0\) are
This question was previously asked in
RRB ALP/Technician 2018 CBT 2 Electronics Mechanic Question Paper (23-Jan-2019) (Shift 1)
The correct answer is
3, 6
Solving the Quadratic Equation
To find the zeros of the equation \(x^2-9x+18=0\), we need to find the values of \(x\) that satisfy the equation. We can solve this using factorization.
Factorization Method
- Find two numbers that multiply to the constant term (18) and add up to the coefficient of the \(x\) term (-9). These numbers are -3 and -6.
- \((-3) \times (-6) = 18\)
- \((-3) + (-6) = -9\)
- Rewrite the equation by splitting the middle term: \(x^2 - 3x - 6x + 18 = 0\)
- Factor by grouping: \(x(x - 3) - 6(x - 3) = 0\)
- Factor out the common binomial term \((x - 3)\): \((x - 3)(x - 6) = 0\)
- Set each factor equal to zero to find the zeros:
- \(x - 3 = 0 \implies x = 3\)
- \(x - 6 = 0 \implies x = 6\)
The zeros of the equation \(x^2-9x+18=0\) are 3 and 6.
This corresponds to Option 4.
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