Write the quadratic equation whose roots are 2 and -3 , and whose leading coefficient is 2 . (Use the letter x to represent the variable.)

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Accepted Answer

Step:1 ：Given the roots of the quadratic equation are 2 and -3, and the leading coefficient is 2.Step:2 ：Using the relationships that the sum of the roots is (-frac{b}{a}) and the product of the roots is (frac{c}{a}), we can find the values of b and c.Step:3 ：Substituting the given values, we get b = -2 and c = -12.Step:4 ：Substituting these values into the standard form of the quadratic equation (ax^2 + bx + c = 0), we get the equation (2x^2 + 2x - 12 = 0).Step:5 ：(boxed{2x^2 + 2x - 12 = 0}) is the final answer.

Answer

Step: 1 ：Given the roots of the quadratic equation are 2 and -3, and the leading coefficient is 2.Step: 2 ：Using the relationships that the sum of the roots is (-frac{b}{a}) and the product of the roots is (frac{c}{a}), we can find the values of b and c.Step: 3 ：Substituting the given values, we get b = -2 and c = -12.Step: 4 ：Substituting these values into the standard form of the quadratic equation (ax^2 + bx + c = 0), we get the equation (2x^2 + 2x - 12 = 0).Step: 5 ：(boxed{2x^2 + 2x - 12 = 0}) is the final answer.

Write the quadratic equation whose roots are 2 and -3 , and whose leading coefficient is 2 . (Use the letter $x$ to represent the variable.)

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