There are different methods of finding the zeros of a quadratic function.
We learn about them with some examples:
What are the zeros of the quadratic function f(x) = 8x^2 – 16x – 15?
The given quadratic function is f(x)=8x2−16x−15
We have to find the zeros of this function.
For this purpose, we will use the Quadratic Formula.
We know that the standard form of a quadratic function is ax2+bx+c .......(1)
where a, b, c are constants.
The Quadratic formula is x=−b±√b2−4ac2a .......(2)
where the sign ± shows that a Quadratic function has two zeros.
Comparing the given Quadratic function with (1) we get,
a=8,b=−16,c=−15
Now putting the values of a, b, c in (2) we get,
x=−b±√b2−4ac2a
or, x=−(−16)±√(−16)2−4(8)(−15)2(8)
or, x=16±√256+48016
or, x=16±√73616
or, x=16±4√4616
or, x=4±√464
or, x=4+√464,4−√464
Therefore the zeros of the quadratic function f(x)=8x2−16x−15 are x=4+√464,4−√464.
Also read: What are the zeroes of the quadratic polynomial 3x^2-48?
Which is a zero of the quadratic function f(x) = 16x^2 + 32x − 9?
To find the zeros of the quadratic function we the Factor method.
Writing the quadratic function as a quadratic equation and factoring we get,
16x2+32x−9=0
or, 16x2+(36−4)x−9=0
or, 16x2+36x−4x−9=0
or, 4x(4x+9)−1(4x+9)=0
or. (4x+9)(4x−1)=0
or, Either 4x+9=0 or 4x−1=0
Either 4x=−9 or 4x=1
Either x=−94 or x=14
Therefore the zeros of the quadratic function f(x) = 16x^2 + 32x − 9 are $ x = \frac{-9}{4} , \frac{1}{4} $
Also read: Find quadratic polynomial whose sum of roots is 0 and the product of roots is 1
What are the zeros of the quadratic function f(x) = 6x^2 + 12x – 7?
Given that f(x)=6x2+12x–7
We use the quadratic formula to find the zeros of a quadratic function.
Comparing the given quadratic function with ax2+bx+c=0 we get
a = 6, b = 12 and c = -7
Now putting these values in (2) we have,
x=−b±√b2−4ac2a
or, x=−12±√(12)2−4(6)(−7)2(6)
or, x=−12±√144+16812
or, x=−12±√31212
or, x=−12±2√7812
or, x=−6±√786
or, x=−6+√786,−6−√786
Therefore the zeros of the quadratic function f(x)=6x2+12x–7 are x=−6+√786,−6−√786
