Ace Algebra 1 with our Extensive Collection of Math Problems

Making a Quadratic Function spit out Integer Outputs for Rational Inputs
Suppose I have a quadratic function
$f (x) = a x^{2} + b x + c, a, b, c \in ℤ$
and I want to find rational (non-integer) values of x for which $f (x) \in Z$ .

afasiask7xg 2022-03-24

Making a Negative Number Possible to Square Root
We are able to solve $x^{2} + 4 = 0$ by square rooting both sides, but if we have $x^{2} = - 4$ we can't solve. Firstly, why? Aren't they equal expressions?
Secondly, if we have $x^{2} = - 4$ , why can't we bring the four to the other side, square root it and then bring it back?

mwombenizhjb 2022-03-24

For which y is $3 x^{4} - 4 x^{2} y + y^{2} < 0$
How does one show that the function $f (x, y) = 3 x^{4} - 4 x^{2} y + y^{2}$ is negative for $x^{2} < y < 3 x^{2}$

London Douglas 2022-03-24

For which a,b,c is the diophantine quadratic equation $a x^{2} + b x + c = y^{2}$ souble?

Alfredo Holmes 2022-03-24

Local extrema of the function $f (x) = x^{3} - 3 α x^{2} + 3 (α^{2} - 1) x + 1$

siliciooy0j 2022-03-24

Line $x + k y + k^{2} = 0$ is tangent to curve $y^{2} = 4 x$ at point P. Find the coordinates of P in terms of k.

Leroy Davidson 2022-03-24

Let $x, y \in R^{n}$ . Let A be a $n \times n$ positive-definite symmetric matrix. Is there a general formula for $x^{T} A x \cdot y^{T} A y$ ?
For example, let $x = [\begin{matrix} 2 \\ 2 \end{matrix}], y = [\begin{matrix} 3 \\ 3 \end{matrix}], A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$
Then $x^{T} A x \cdot y^{T} A y = 8 \cdot 18 = 144$
This is equal to $2 {(x \circ y)}^{T} A (x \circ y)$ where $(x \circ y) = [\begin{matrix} 6 \\ 6 \end{matrix}]$ is the Hadamard product of x,y.
It seems that $x^{T} A x \cdot y^{T} A y = 2 {(x \circ y)}^{T} A (x \circ y)$ also works for $x = [\begin{matrix} 5 \\ 5 \end{matrix}], y = [\begin{matrix} 7 \\ 7 \end{matrix}]$ . Is this true in the general case, and if so, how do I prove it? If not, how can I find and prove a general formula?

diartrosiwk8o 2022-03-24

Let $P (z) = a z^{2} + b z + c$ , where a,b,c are complex numbers.
1) If P(z) is real for all real z then show that a,b,c are real numbers.
2) In addition to (1) above, assume that P(z) is not real whenever z is not real. Show that $a = 0$ .

Coradossi7xod 2022-03-24

Let $x_{1}, x_{2} \in R$ be the roots of the equation $x^{2} + p x + q = 0$ . Find p and q if it is known that $x_{1} + 1 and x_{2} + 1$ are the roots of the equation $x^{2} - p^{2} x + p q = 0$ .

Octavio Chen 2022-03-24

Let $< a_{n} >$ and $< b_{n} >$ be the arithmetic progression sequences each with common difference 2 such that $a_{1} < b_{1}$ and let $c_{n} = \sum_{{k = 1}}^{n} a_{k}$ and $d_{n} = \sum_{{k = 1}}^{n} b_{k}$ . Suppose the points $A_{n} (a_{n}, c_{n})$ and $B_{n} (b_{n}, d_{n})$ are all lying on the parabola, $y = p x^{2} + q x + r$ , then find value of p, q.

mwombenizhjb 2022-03-24

Let p(x) be $a x^{2} - b x + c = 0$ where a,b,c are natural nos. and it has roots lying in the interval (1,2), then find the minimum value of a,b,c individually.

dayncNonow04r 2022-03-24

From $a x^{2} + b x + c$ (quadratic formula) 3 points (5,500),(3,375),(12,980) I solved
$25 a + 5 b + c = 500$
$9 a + 3 b + c = 375$
$144 a + 12 b + c = 980$
s it possible to solve it without a calculator (for the simulateneous equations) If yes, How can I do it?

Y=10^x

Maykyllah Jane Rojo2022-03-23

At the beginning of the year, there are 7650 individuals in a population of beavers whose per capita rate of for the year is 0.18. What is its population growth rate at the end of the year?

Destinee Hensley 2022-03-23

Solve, please, the equation where v is a real number
${(v - 8)}^{3} - 64 = 0$

dotzis16xd 2022-03-23

Solve, please
$| \frac{3 x - 4}{2 x - 1} | < 1$

Lucian Ayers 2022-03-23

Solve using the quadratic formula
$2 x^{2} - x = 9$

zatajuxoqj 2022-03-23

Solve this inequality
$\frac{1}{x^{2} - 14 x + 40} \leq 0$

Paula Good 2022-03-23

Solve the inequality
$\frac{- 5 x {(x - 3)}^{2}}{2 + x} \leq 0$

aidinacol7 2022-03-23

Solve the equation
$4 x^{4} + 3 x^{2} - 1 = 0$

When you are a high school student or someone already enrolled in college, even those simple research projects will include Algebra 1 equations, which means that getting some help cannot be avoided. Thankfully, you can access Algebra 1 problems and answers free of charge, which will let you see what Algebra 1 practice problems can be used for certain questions. Just remember to check calculations twice as these can easily get complex. The majority of Algebra 1 answers will be familiar to most students dealing with financial concepts as it is not related to advanced Math problems in most scenarios.

Algebra I

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