If p(x) = x² − 12x + 36, what is the distinct real zero?
Answer and explanation
Correct answer: 6
The governing concept is that repeated roots are counted once when the question asks for distinct zeroes. Recognise the perfect-square trinomial: p(x) = x² − 12x + 36 = (x − 6)². Setting p(x) equal to zero gives (x − 6)² = 0, so x − 6 = 0 and x = 6. Both algebraic roots coincide, meaning the polynomial has one distinct real zero, 6, with multiplicity two. Graphically, the parabola touches the x-axis at the single point (6, 0) rather than crossing it at two different points. Therefore option A is correct. The value −6 has the wrong sign, 12 is the coefficient magnitude rather than the root, and option D is false because x = 6 is a valid real solution.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The governing concept is that repeated roots are counted once when the question asks for distinct zeroes. Recognise the perfect-square trinomial: p(x) = x² − 12x + 36 = (x − 6)². Setting p(x) equal to zero gives (x − 6)² = 0, so x − 6 = 0 and x = 6. Both algebraic roots coincide, meaning the polynomial has one distinct real zero, 6, with multiplicity two. Graphically, the parabola touches the x-axis at the single point (6, 0) rather than crossing it at two different points. Therefore option A is correct. The value −6 has the wrong sign, 12 is the coefficient magnitude rather than the root, and option D is false because x = 6 is a valid real solution.
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.
