how to find the x intercept of d(x)=9x^2-4x+7
c'mon. It's just finding roots of a quadratic.
Since the discriminant is 16-4*9*7 < 0, there is no x-intercept
yeah i know but how will you know when to use this discriminant formula ?
To find the x-intercept of a function, we need to find the values of x where the function crosses or touches the x-axis. Mathematically, we can find the x-intercept by setting the value of the function equal to zero and solving for x.
In the case of the function d(x) = 9x^2 - 4x + 7, we need to set d(x) equal to zero:
0 = 9x^2 - 4x + 7
To solve this quadratic equation, we can use either factoring, completing the square, or the quadratic formula. Factoring is not straightforward in this case, so let's solve it using the quadratic formula.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Comparing our equation to the standard form, we have:
a = 9, b = -4, and c = 7.
Substituting these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(9)(7))) / (2(9))
Simplifying further,
x = (4 ± √(16 - 252)) / 18
x = (4 ± √(-236)) / 18
The term inside the square root, -236, is negative, which means there are no real solutions. In other words, the quadratic function d(x) = 9x^2 - 4x + 7 does not intersect or touch the x-axis. Therefore, there are no x-intercepts for this function.