If p(x) = x^2 - 15x + 56, what is the distance between the zeroes of the graph?
Answer and explanation
Correct answer: 1
The graph meets the x-axis at the zeroes of the polynomial. To find them, factor the quadratic: x^2 - 15x + 56 = (x - 7)(x - 8), since 7 + 8 = 15 and 7 × 8 = 56. Therefore the x-intercepts, or zeroes, are 7 and 8. The distance between two points on the x-axis is the absolute difference of their x-coordinates: |8 - 7| = 1. Hence option A is correct. The values 7 and 8 are the individual zeroes, not their separation. The number 15 is their sum, while 56 is their product, so options B, C and D represent related but incorrect quantities.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The graph meets the x-axis at the zeroes of the polynomial. To find them, factor the quadratic: x^2 - 15x + 56 = (x - 7)(x - 8), since 7 + 8 = 15 and 7 × 8 = 56. Therefore the x-intercepts, or zeroes, are 7 and 8. The distance between two points on the x-axis is the absolute difference of their x-coordinates: |8 - 7| = 1. Hence option A is correct. The values 7 and 8 are the individual zeroes, not their separation. The number 15 is their sum, while 56 is their product, so options B, C and D represent related but incorrect quantities.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
