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If the roots of the equation x^2 - 2ax + a^2 + a - 3=0 are real and less than 3 then what is the range in which a lies?
Ref: https://edurev.in/question/483538/If-the-roots-of-the-equation-x-2-2ax-a-2-a-30-are-real-and-less-than-3-then-what-is-the-range-in-whi


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1. What is a simple algebraic equation?
Ans. A simple algebraic equation is an equation in which there is only one variable and the highest power of the variable is 1. It can be represented in the form of ax + b = 0, where a and b are constants.
2. How can we solve simple algebraic equations?
Ans. To solve a simple algebraic equation, we need to isolate the variable on one side of the equation. We can do this by performing the same operation on both sides of the equation. The goal is to simplify the equation until we obtain the value of the variable.
3. Can you provide an example of solving a simple algebraic equation?
Ans. Sure! Let's solve the equation 2x + 5 = 13. Subtracting 5 from both sides, we get: 2x = 8 Dividing both sides by 2, we get: x = 4 So, the solution to the equation is x = 4.
4. Are there any shortcuts or tricks to solve simple algebraic equations quickly?
Ans. Yes, there are some shortcuts or tricks that can help solve simple algebraic equations quickly. One such trick is to use the concept of balancing both sides of the equation by performing inverse operations. By performing the same operation on both sides, we can simplify the equation and find the value of the variable more efficiently.
5. Can simple algebraic equations be solved graphically?
Ans. Yes, simple algebraic equations can be solved graphically. The equation ax + b = 0 represents a straight line in a coordinate plane. By plotting the points on the line and finding the x-coordinate of the point where the line intersects the x-axis, we can determine the solution to the equation.
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