Square Roots of Quadratic Equations - Definition & Examples
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- (Video) The Square Root Property by mathman1024 This video by mathman1024 explains the square root property. Summary\large{\text{Summary}}Summary The square root property states…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman
- There are several way to approach quadratic equations. Before discussing how to solve them, let's review quadratic equations. A quadratic equation is an equation that takes the …
By Victoria Rodriguez, Alex Federspiel, Jonathan Heller, Anusha Rahman
- Solve Quadratic Equations by Square Root There are a few important things to remember when you need to solve a quadratic equation using a square root. For one, when you take the…
By Caroline K
Problems 50
- Solve the equation for rrr, assuming hhh is positive. V=13 πr2hV=\frac{1}{3}\ \pi r^2hV=31 πr2h (Note: π=3.14…\pi=3.14\dotsπ=3.14… is a constant. In a cylinder, VVV stands for …
- The area of a circle is 16π16\pi16π. Use this to find the radius of the circle.
- The distance formula is d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2−x1)2+(y2−y1)2. Solve for y1y_1y1.
- The Pythagorean theorem is given by: a2+b2=c2a^2+b^2=c^2a2+b2=c2. Solve for aaa.
- The surface area of a cone can be found using the following equation. SA=πrr2+h2S_A=\pi r\sqrt{r^2+h^2}SA=πrr2+h2 Solve for hhh.
- The distance between two points is given by the formula d=(x2−x1)2+(y2−y1)2.d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.d=(x2−x1)2+(y2−y1)2. If you know the distance between two point…
- How many real solutions does the equation ∣x2−2∣=1|x^2 - 2| = 1∣x2−2∣=1 have?
- How many real solutions does the equation ∣x2−2∣=2|x^2 - 2| = 2∣x2−2∣=2 have?
- How many real solutions does the equation ∣x2−2∣=3|x^2 - 2| = 3∣x2−2∣=3 have?
- What is the negative solution ppp to the equation (1−p)2=4p2(1-p)^2=4p^2(1−p)2=4p2?
- True or False\text{True or False}True or False === If a quadratic equation is in the form x2+c=0x^2+c = 0x2+c=0 where c>0c>0c>0, then there are two real solutions for xxx.
- Solve for xxx. Mark all possible solutions below. x2=36x^2=36x2=36
- Solve for xxx. x2=81x^2=81x2=81
- Suppose we have a sequence which, for n≥1n \ge 1n≥1, satisfies an=(an−1)2+(an−1)−4a_n = (a_{n-1})^2 + (a_{n-1}) - 4an=(an−1)2+(an−1)−4. If this sequence is periodic with fund…
- Suppose that the second term of a geometric sequence is 333 and the fourth term is 272727. List all possible values for the first term of the sequence.
- A circle has a radius of 555. It is 85\frac8558 times as large (in area) as a second circle. What is the radius of this other circle, rounded to the nearest hundredth?
- How many real solutions does x2=−2017x^2 = -2017x2=−2017 have?
- How many real solutions does x2=0x^2 = 0x2=0 have?
- How many real solutions does x2=2017x^2 = 2017x2=2017 have?
- How many real solutions does x2=(x−1)2x^2 = (x-1)^2x2=(x−1)2 have?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c, what is the maximum number of real-numbered roots the function can have?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c, what is the minimum number of real-numbered roots the function can have?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c and has exactly 111 real-numbered root, which one of the following must be true?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c and has exactly 222 real-numbered roots, which one of the following must be true?
- If fff is a quadratic function of the form ax2+cax^2+cax2+c and no real-numbered roots, which one of the following must be true?
- Solve for xxx. x2=25x^2=25x2=25
- Catie is preparing boxes of cookies to give out to her friends and family during the holiday season. For easy counting, she has arranged the boxes into rows and columns, with an…
- Find xxx such that x2=8x.\frac{x}{2}=\frac{8}{x}.2x=x8.
- Find xxx in terms of aaa: xa=ax\frac{x}{a}=\frac{a}{x}ax=xa
- Here's an equation for error propagation in circuits: αR=R(αVV)2+(αII)2.\alpha_R = R\sqrt{\left(\frac{\alpha_V}{V}\right)^2 + \left(\frac{\alpha_I}{I}\right)^2}.αR=R(VαV)2+(I…
- Solve for the speed of light, ccc in the following equation. E=mc2E=mc^2E=mc2
- Isolate sss as a function of AAA.
- Find the largest possible value of xxx such that x2−5=20.x^2-5=20.x2−5=20.
- Find all values of xxx such that x2−46=2.\frac{x^2-4}{6}=2.6x2−4=2.
- Find all xxx such that 2+x26=3.\frac{2+x^2}{6}=3.62+x2=3.
- Solve for xxx, given that xxx is positive: 2x2=2882x^2=2882x2=288.
- What is the positive solution ppp to the equation (1−p)2=4p2(1-p)^2=4p^2(1−p)2=4p2?
- If (x+1)2=0(x+1)^2 = 0(x+1)2=0, then which value of xxx solves the equation?
- If x2=3x^2 = 3x2=3, then the possible real values of xxx are...
- If 2x2=182x^2 = 182x2=18, then the possible real values of xxx are...
- If 3x2=183x^2 = 183x2=18, then the possible real values of xxx are...
- If 9x2=−π29x^2 = -\pi^29x2=−π2, then the possible real values of xxx are...
- If x2+2x+1=3x^2+2x+1 = 3x2+2x+1=3, then the possible real values of xxx are...
- If 2x2+8x+8=122x^2+8x+8 = 122x2+8x+8=12, then the possible real values of xxx are...
- Find all values of xxx such that (x−2)26=2.\frac{(x-2)^2}{6}=2.6(x−2)2=2.
- Using the equation ANNA=25ANNA=25ANNA=25 where AAA and NNN are positive variables, write NNN in terms of MMM.
- Which of the following values are valid solutions to this equation? x2=4x^2 =4x2=4
- If a2=ba^2 = ba2=b, where bbb is positive, what can we say for sure about aaa?
- I'm thinking of a number where if I take 333 less than 444 times this number, then square it, I get 494949. \\ What number(s) could I be thinking of? (You can choose more than o…
- I'm thinking of a positive number. When I take the difference of this number and 333, and then square the result, I end up with 161616. What number am I thinking of?