Grade 10 Exam > Grade 10 Questions > If the zeros of a polynomial are 3 and -5, th...
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If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.
- a)(8, 0) and (-4, 0)
- b)(3, -3) and (-5, 5)
- c)(-3, 0) and (5, 0)
- d)(3, 0) and (-5, 0)
Correct answer is option 'D'. Can you explain this answer?
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If the zeros of a polynomial are 3 and -5, then they cut the x-axis at...
Since, the zeros of the polynomial are 3 and -5.
Therefore, x = 3 and x = -5 and they cut the x-axis so the y-coordinate will be zero.
Hence, the points it cuts the x-axis will be (3, 0) and (-5, 0).
Therefore, x = 3 and x = -5 and they cut the x-axis so the y-coordinate will be zero.
Hence, the points it cuts the x-axis will be (3, 0) and (-5, 0).
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If the zeros of a polynomial are 3 and -5, then they cut the x-axis at...
Solution:
Given that the zeros of the polynomial are 3 and -5.
To find the points where the polynomial cuts the x-axis, we need to find the corresponding y-values when x is equal to the zeros.
Let's consider the zero 3.
When x = 3, the polynomial becomes zero. Therefore, we can substitute x = 3 into the polynomial and solve for the corresponding y-value.
Let's assume the polynomial is of the form ax^2 + bx + c.
Substituting x = 3, we get:
a(3)^2 + b(3) + c = 0
9a + 3b + c = 0
Similarly, let's consider the zero -5.
When x = -5, the polynomial becomes zero. Substituting x = -5 into the polynomial, we get:
a(-5)^2 + b(-5) + c = 0
25a - 5b + c = 0
Now, we have two equations:
9a + 3b + c = 0 ...(Equation 1)
25a - 5b + c = 0 ...(Equation 2)
To solve these equations, we can use the method of substitution or elimination.
Subtracting Equation 1 from Equation 2, we get:
16a - 8b = 0
16a = 8b
a = (8/16)b
Simplifying, we get:
a = (1/2)b
Now, we can substitute the value of a in Equation 1:
9(1/2)b + 3b + c = 0
(9/2)b + 3b + c = 0
(9/2 + 6/2)b + c = 0
(15/2)b + c = 0
We can see that for any value of b, c = -(15/2)b is satisfied.
Therefore, the polynomial can be written as:
f(x) = (1/2)b(x^2 - 15)
So, the polynomial cuts the x-axis at the points (3, 0) and (-5, 0).
Hence, the correct answer is option D: (3, 0) and (-5, 0).
Given that the zeros of the polynomial are 3 and -5.
To find the points where the polynomial cuts the x-axis, we need to find the corresponding y-values when x is equal to the zeros.
Let's consider the zero 3.
When x = 3, the polynomial becomes zero. Therefore, we can substitute x = 3 into the polynomial and solve for the corresponding y-value.
Let's assume the polynomial is of the form ax^2 + bx + c.
Substituting x = 3, we get:
a(3)^2 + b(3) + c = 0
9a + 3b + c = 0
Similarly, let's consider the zero -5.
When x = -5, the polynomial becomes zero. Substituting x = -5 into the polynomial, we get:
a(-5)^2 + b(-5) + c = 0
25a - 5b + c = 0
Now, we have two equations:
9a + 3b + c = 0 ...(Equation 1)
25a - 5b + c = 0 ...(Equation 2)
To solve these equations, we can use the method of substitution or elimination.
Subtracting Equation 1 from Equation 2, we get:
16a - 8b = 0
16a = 8b
a = (8/16)b
Simplifying, we get:
a = (1/2)b
Now, we can substitute the value of a in Equation 1:
9(1/2)b + 3b + c = 0
(9/2)b + 3b + c = 0
(9/2 + 6/2)b + c = 0
(15/2)b + c = 0
We can see that for any value of b, c = -(15/2)b is satisfied.
Therefore, the polynomial can be written as:
f(x) = (1/2)b(x^2 - 15)
So, the polynomial cuts the x-axis at the points (3, 0) and (-5, 0).
Hence, the correct answer is option D: (3, 0) and (-5, 0).
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If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.a)(8, 0) and (-4, 0)b)(3, -3) and (-5, 5)c)(-3, 0) and (5, 0)d)(3, 0) and (-5, 0)Correct answer is option 'D'. Can you explain this answer?
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If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.a)(8, 0) and (-4, 0)b)(3, -3) and (-5, 5)c)(-3, 0) and (5, 0)d)(3, 0) and (-5, 0)Correct answer is option 'D'. Can you explain this answer? for Grade 10 2024 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.a)(8, 0) and (-4, 0)b)(3, -3) and (-5, 5)c)(-3, 0) and (5, 0)d)(3, 0) and (-5, 0)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Grade 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.a)(8, 0) and (-4, 0)b)(3, -3) and (-5, 5)c)(-3, 0) and (5, 0)d)(3, 0) and (-5, 0)Correct answer is option 'D'. Can you explain this answer?.
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