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mash [69]
3 years ago
5

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

Mathematics
2 answers:
charle [14.2K]3 years ago
5 0
5/2+(1/2)*sqrt(31), 5/2-(1/2)*sqrt(31)
Sholpan [36]3 years ago
3 0
<h2>Answer:</h2>

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

               x=\dfrac{5+\sqrt{31}}{2}\ ,\ x=\dfrac{5-\sqrt{31}}{2}    

<h2>Step-by-step explanation:</h2>

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=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

Here we have:

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

Hence, the solution is:

x=\dfrac{-(-10)\pm \sqrt{(-10)^2-4\times 2\times (-3)}}{2\times 2}\\\\\\x=\dfrac{10\pm \sqrt{100+24}}{4}\\\\\\x=\dfrac{10\pm \sqrt{124}}{4}\\\\\\x=\dfrac{10\pm 2\sqrt{31}}{4}\\\\\\x=\dfrac{5\pm \sqrt{31}}{2}    

Hence,

x=\dfrac{5+\sqrt{31}}{2} and x=\dfrac{5-\sqrt{31}}{2}

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