If p(x) = x² + x − 6, what are its real zeroes?
Answer and explanation
Correct answer: 2 and −3
The governing concept is that zeroes are the values of x that make the polynomial equal to zero. Factor the expression by finding two numbers whose product is −6 and whose sum is 1: these are 3 and −2. Thus x² + x − 6 = (x + 3)(x − 2). Applying the zero-product property, either x + 3 = 0, giving x = −3, or x − 2 = 0, giving x = 2. Therefore the real zeroes are 2 and −3, so option A is correct. Option B would result from changing both signs, option C confuses the constant and coefficient with roots, and option D is false because two real solutions have been obtained directly by factorisation.
Frequently asked questions
What is the correct answer to this question?
2 and −3
Why is this the correct answer?
The governing concept is that zeroes are the values of x that make the polynomial equal to zero. Factor the expression by finding two numbers whose product is −6 and whose sum is 1: these are 3 and −2. Thus x² + x − 6 = (x + 3)(x − 2). Applying the zero-product property, either x + 3 = 0, giving x = −3, or x − 2 = 0, giving x = 2. Therefore the real zeroes are 2 and −3, so option A is correct. Option B would result from changing both signs, option C confuses the constant and coefficient with roots, and option D is false because two real solutions have been obtained directly by factorisation.
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.
