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.
Similar Questions
- If $x^2 + kx + k = 0$ has no solution, then the value of k will satisfy:
- 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:
$4x^2 + 4x - 3 = 0$ - Which of the following is a quadratic equation?
- 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:
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
