Write the quadratic equation whose roots are −1 and 4, and whose leading coefficient is 4.(Use the letter x to represent the variable.)
Question
Write the quadratic equation whose roots are −1 and 4, and whose leading coefficient is 4.
(Use the letter x to represent the variable.)
Solution
The quadratic equation can be found using the formula:
f(x) = a(x - r1)(x - r2)
where r1 and r2 are the roots of the equation, and a is the leading coefficient.
Given that the roots are -1 and 4, and the leading coefficient is 4, we can substitute these values into the formula:
f(x) = 4(x - (-1))(x - 4)
Simplify the equation:
f(x) = 4(x + 1)(x - 4)
Expand the equation:
f(x) = 4(x^2 - 4x + x - 4)
Simplify the equation:
f(x) = 4x^2 - 12x - 16
So, the quadratic equation whose roots are -1 and 4, and whose leading coefficient is 4 is f(x) = 4x^2 - 12x - 16.
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