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Aryan Pandey1
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Let f(x) , g(x) and h(x) be the quadratic polynomials having positive leading coefficients an real and distinct roots. If each pair of them has a common root , then find the roots of f(x)+g(x)+h(x) = 0.
Aryan Pandey said:Let f(x) , g(x) and h(x) be the quadratic polynomials having positive leading coefficients an real and distinct roots. If each pair of them has a common root , then find the roots of f(x)+g(x)+h(x) = 0.
The process for finding the roots of f(x)+g(x)+h(x) = 0 involves setting the equation equal to 0 and using algebraic methods to solve for the value(s) of x that make the equation true. This may involve factoring, the quadratic formula, or other techniques depending on the specific equation.
Yes, for example, let's say we have the equation x^2 + 2x + 1 = 0. We can factor this equation to (x+1)(x+1) = 0, which gives us two solutions: x = -1. Therefore, the roots of this equation are x = -1.
An equation will have multiple roots if it can be factored into multiple linear factors. For example, the equation x^2 - 4 = 0 has two roots, x = 2 and x = -2, because it can be factored into (x+2)(x-2) = 0.
Yes, there are some shortcuts that can be used for certain types of equations. For example, if the equation is a perfect square trinomial, you can use the formula (a + b)^2 = a^2 + 2ab + b^2 to find the roots. Additionally, if the equation is a cubic or quartic equation, there are specific formulas that can be used to find the roots.
Yes, you can use a graph to estimate the roots of an equation. The x-intercepts on the graph represent the points where the equation equals 0, so you can visually determine the approximate values of the roots. However, it is important to note that this method is not always accurate and should be used in conjunction with algebraic methods.