Using the factorisation method, what are the roots of x² − 9x + 20 = 0?
Answer and explanation
Correct answer: x = 4, 5
The governing concept is factorisation together with the zero-product property. We seek two numbers whose product is 20 and whose sum is 9; these numbers are 4 and 5. Therefore x² − 9x + 20 can be written as x² − 4x − 5x + 20 = (x − 4)(x − 5). The equation becomes (x − 4)(x − 5) = 0. By the zero-product property, either x − 4 = 0 or x − 5 = 0, giving x = 4 or x = 5. Option B would produce negative roots and a positive sum in the factorised expression, not the required middle coefficient. Options C and D have products or sums that do not match 20 and 9. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
x = 4, 5
Why is this the correct answer?
The governing concept is factorisation together with the zero-product property. We seek two numbers whose product is 20 and whose sum is 9; these numbers are 4 and 5. Therefore x² − 9x + 20 can be written as x² − 4x − 5x + 20 = (x − 4)(x − 5). The equation becomes (x − 4)(x − 5) = 0. By the zero-product property, either x − 4 = 0 or x − 5 = 0, giving x = 4 or x = 5. Option B would produce negative roots and a positive sum in the factorised expression, not the required middle coefficient. Options C and D have products or sums that do not match 20 and 9. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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