find the zeros of f,f(x) = 2x2 + x − 21
x= ? larger value
x= ? smaller value
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that said, here's a tip:
2x^2+x-21 = (2x+7)(x-3)
To find the zeros of the function f(x) = 2x^2 + x - 21, we need to find the values of x for which f(x) equals zero. In other words, we need to solve the equation 2x^2 + x - 21 = 0.
There are various methods to solve this quadratic equation, but one common method is to use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the equation 2x^2 + x - 21 = 0, a = 2, b = 1, and c = -21. Plugging these values into the quadratic formula, we get:
x = (-(1) ± √((1)^2 - 4(2)(-21))) / (2(2))
Simplifying further:
x = (-1 ± √(1 + 168)) / 4
Now, we can calculate the two possible values for x:
x1 = (-1 + √169) / 4 = (8 / 4) = 2
x2 = (-1 - √169) / 4 = (-10 / 4) = -2.5
Therefore, the larger value of x is 2 and the smaller value is -2.5.