Grade 10 Exam > Grade 10 Questions > The graph of the polynomial 4x2- 8x + 3 cuts ...
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The graph of the polynomial 4x2 - 8x + 3 cuts the x-axis at ________ and ________ points.
- a)(3/4, 0), (1/2, 0)
- b)(3/2, 0), (1/2, 0)
- c)(3/2, 0), (1/6, 0)
- d)(7/2, 0), (3/2, 0)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The graph of the polynomial 4x2- 8x + 3 cuts the x-axis at ________ an...
The graph of the polynomial cuts the x-axis. Only the zeros of the polynomial cut the x-axis.
4x2 - 8x + 3 = 0
4x2 - 6x - 2x + 3 = 0
2x(2x - 3) - 1(2x - 3) = 0
(2x - 3)(2x - 1) = 0
x = 3/2, 1/2
Hence, the graph of the polynomial cuts the x-axis at (3/2, 0) and (1/2, 0).
4x2 - 8x + 3 = 0
4x2 - 6x - 2x + 3 = 0
2x(2x - 3) - 1(2x - 3) = 0
(2x - 3)(2x - 1) = 0
x = 3/2, 1/2
Hence, the graph of the polynomial cuts the x-axis at (3/2, 0) and (1/2, 0).
Most Upvoted Answer
The graph of the polynomial 4x2- 8x + 3 cuts the x-axis at ________ an...
Understanding the Polynomial Equation
To determine where the graph of the polynomial \(4x^2 - 8x + 3\) cuts the x-axis, we need to find the x-intercepts. The x-intercepts occur where the polynomial equals zero:
\[
4x^2 - 8x + 3 = 0
\]
Applying the Quadratic Formula
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For our polynomial, the coefficients are:
- \(a = 4\)
- \(b = -8\)
- \(c = 3\)
Now, substitute these values into the formula:
Calculating the Discriminant
First, calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = (-8)^2 - 4(4)(3)
\]
Calculating this gives:
\[
64 - 48 = 16
\]
Since the discriminant is positive, we will have two distinct real roots.
Finding the Roots
Now, substitute back into the quadratic formula:
\[
x = \frac{8 \pm \sqrt{16}}{8}
\]
This simplifies to:
\[
x = \frac{8 \pm 4}{8}
\]
Calculating the two roots:
1. \(x = \frac{12}{8} = \frac{3}{2}\)
2. \(x = \frac{4}{8} = \frac{1}{2}\)
Conclusion
The graph of the polynomial \(4x^2 - 8x + 3\) intersects the x-axis at:
- \((\frac{3}{2}, 0)\)
- \((\frac{1}{2}, 0)\)
Thus, the correct answer is option **'B'**: \((\frac{3}{2}, 0)\) and \((\frac{1}{2}, 0)\).
To determine where the graph of the polynomial \(4x^2 - 8x + 3\) cuts the x-axis, we need to find the x-intercepts. The x-intercepts occur where the polynomial equals zero:
\[
4x^2 - 8x + 3 = 0
\]
Applying the Quadratic Formula
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For our polynomial, the coefficients are:
- \(a = 4\)
- \(b = -8\)
- \(c = 3\)
Now, substitute these values into the formula:
Calculating the Discriminant
First, calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = (-8)^2 - 4(4)(3)
\]
Calculating this gives:
\[
64 - 48 = 16
\]
Since the discriminant is positive, we will have two distinct real roots.
Finding the Roots
Now, substitute back into the quadratic formula:
\[
x = \frac{8 \pm \sqrt{16}}{8}
\]
This simplifies to:
\[
x = \frac{8 \pm 4}{8}
\]
Calculating the two roots:
1. \(x = \frac{12}{8} = \frac{3}{2}\)
2. \(x = \frac{4}{8} = \frac{1}{2}\)
Conclusion
The graph of the polynomial \(4x^2 - 8x + 3\) intersects the x-axis at:
- \((\frac{3}{2}, 0)\)
- \((\frac{1}{2}, 0)\)
Thus, the correct answer is option **'B'**: \((\frac{3}{2}, 0)\) and \((\frac{1}{2}, 0)\).
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The graph of the polynomial 4x2- 8x + 3 cuts the x-axis at ________ and ________ points.a)(3/4, 0), (1/2, 0)b)(3/2, 0), (1/2, 0)c)(3/2, 0), (1/6, 0)d)(7/2, 0), (3/2, 0)Correct answer is option 'B'. Can you explain this answer?
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