The equation whose roots are 4 and 5, is

Options

A. `x^2-9x-20=0`
B. `x^2-9x+20=0`
C. `x^2+9x+20=0`
D. `x^22+9x-20=0`

Answer

To find the equation whose roots are 4 and 5, we can follow these steps:

### Step 1: Understand the relationship between roots and factors
If a quadratic equation has roots \( r_1 \) and \( r_2 \), then it can be expressed in the form:
\[ (x - r_1)(x - r_2) = 0 \]
In this case, the roots are 4 and 5.

### Step 2: Substitute the roots into the equation
Substituting the roots into the formula gives us:
\[ (x - 4)(x - 5) = 0 \]

### Step 3: Expand the equation
Now, we will expand the equation:
\[ (x - 4)(x - 5) = x^2 - 5x - 4x + 20 \]
Combining like terms results in:
\[ x^2 - 9x + 20 = 0 \]

### Step 4: Write the final equation
Thus, the equation whose roots are 4 and 5 is:
\[ x^2 - 9x + 20 = 0 \]

### Conclusion
The final quadratic equation is:
\[ x^2 - 9x + 20 = 0 \]

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