Can a quadratic polynomial equation with real coefficients have one real solution and one complex solution? If so,
1 answer:
Answer:
No
Step-by-step explanation:
We have to find that a quadratic polynomial equation with real coefficient can have one real solution and one complex solution.
quadratic equation is given by
It can be written as the product of linear factors
Where are solutions of the given polynomial equation.
No , a quadratic polynomial equation can not have one real solution and one complex solution because complex root are always in paired not a single.
A quadratic equation have two roots only.
If a quadratic equation have complex root then the equation have both complex root .
If a equation have real root then it have both real.
Therefore, a quadratic equation can not have one real and one compelx solution.
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The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
<h3>How does the transformation of a function happen?</h3>The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units, y=f(x+c) (same output, but c units earlier)
- Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f(\dfrac{x}{k})
The function f(x)=x^(1/3) is transformed to form the function of h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,
Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)
Up by 5 units ⇒ (2x)^(1/3) + 5
Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
Learn more about Transforming functions:
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Answer:
A=$265.42
Step-by-step explanation:
The formula to apply here is;
where;
A=amount at the end
P=principal amount=$250
r=rate of interest=0.06%
n=number of compounding per year=12
t=total number of years=1