Find the roots of the function (f(x) = 2x^2 - 5x - 3).

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Accepted Answer

Step:1 ：To find the roots of the function, we need to solve for (x) in the equation (f(x) = 2x^2 - 5x - 3 = 0).Step:2 ：We will use the quadratic formula, which is given by (x = frac{-b pm sqrt{b^2 - 4ac}}{2a}). In this case, (a = 2), (b = -5), and (c = -3).Step:3 ：Substituting these values into the quadratic formula gives (x = frac{-(-5) pm sqrt{(-5)^2 - 4*2*(-3)}}{2*2}).Step:4 ：Simplifying the above expression gives (x = frac{5 pm sqrt{25 + 24}}{4}).Step:5 ：Further simplifying gives (x = frac{5 pm sqrt{49}}{4}).Step:6 ：Taking the square root of 49 gives 7, so (x = frac{5 pm 7}{4}).Step:7 ：This gives two possible solutions for (x), which are (x = frac{5 + 7}{4} = 3) and (x = frac{5 - 7}{4} = -0.5).

Answer

Step: 1 ：To find the roots of the function, we need to solve for (x) in the equation (f(x) = 2x^2 - 5x - 3 = 0).Step: 2 ：We will use the quadratic formula, which is given by (x = frac{-b pm sqrt{b^2 - 4ac}}{2a}). In this case, (a = 2), (b = -5), and (c = -3).Step: 3 ：Substituting these values into the quadratic formula gives (x = frac{-(-5) pm sqrt{(-5)^2 - 4*2*(-3)}}{2*2}).Step: 4 ：Simplifying the above expression gives (x = frac{5 pm sqrt{25 + 24}}{4}).Step: 5 ：Further simplifying gives (x = frac{5 pm sqrt{49}}{4}).Step: 6 ：Taking the square root of 49 gives 7, so (x = frac{5 pm 7}{4}).Step: 7 ：This gives two possible solutions for (x), which are (x = frac{5 + 7}{4} = 3) and (x = frac{5 - 7}{4} = -0.5).

Find the roots of the function $f (x) = 2 x^{2} - 5 x - 3$ .

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Popular Problems

Find the roots of the function f(x)=2x2−5x−3.

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Popular Problems

Find the roots of the function $f (x) = 2 x^{2} - 5 x - 3$ .