Question

What are the zeros of the quadratic function f(x)=2x^2-10x-3

Answer 1

5/2+(1/2)*sqrt(31), 5/2-(1/2)*sqrt(31)

Answer 2

The zeros of the quadratic function
`f(x)=2x^2-10x-3` are:

`x=(5+√(31))/(2)\ ,\ x=(5-√(31))/(2)`

Explanation:

Zeros of a function are the possible x values of the function for which the function is equal to zero.

i.e. all those x for which f(x)=0

We are given a function f(x) by:

`f(x)=2x^2-10x-3`

Now, f(x)=0

`2x^2-10x-3=0`

We know that the solution of the quadratic equation of the type:

`ax^2+bx+c=0` is given by:

`x=(-b\pm √(b^2-4ac))/(2a)`

Here we have:

a=2, b= -10 and c= -3

Hence, the solution is:

`x=(-(-10)\pm √((-10)^2-4* 2* (-3)))/(2* 2)\\\\\\x=(10\pm √(100+24))/(4)\\\\\\x=(10\pm √(124))/(4)\\\\\\x=(10\pm 2√(31))/(4)\\\\\\x=(5\pm √(31))/(2)`

Hence,

`x=(5+√(31))/(2)` and
`x=(5-√(31))/(2)`