The zero of the quadratic function f(x) = 16x2 + 32x − 9 is x = ( -9 / 4) and x = ( 1 / 4).
What is a quadratic equation?
The quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
The locations when a polynomial equals zero overall are known as its zeros. Simply put, we can state that the zeros of a polynomial are x values.
A zero of a function is the value of x for which f(x) = 0. The given quadratic equation will be solved as below.
f(x) = 16x²+ 32x - 9 = 0
Split the middle part 32x into -4x and 36x to factor the equation.
16x² - 4x + 36x - 9 = 0
Now separate the terms by taking common.
(16x² - 4x) + (36x - 9) = 0
4x(4x - 1) + 9(4x - 1) = 0
(4x + 9)(4x - 1) = 0
Equate the two parts of the equation with zero.
4x + 9 = 0 and 4x - 1 = 0
4x = -9 and 4x = 1
The values of x are:-
x = -9/4 and x = 1/4
Hence, the zeroes of the equation will be x = -9/4 and x = 1/4.
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