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ollegr [7]
3 years ago
6

Use the quadratic formula to determine the exact solutions to the equation.

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
6 0

ANSWER

x = \frac{5}{4}   -  \frac{  \sqrt{ 17} }{4}

or

x = \frac{5}{4}  +  \frac{  \sqrt{ 17} }{4}

EXPLANATION

The given equation is:

2 {x}^{2} - 5x + 1= 0

Comparing this to

a {x}^{2}  + bx + c = 0

we have a=2, b=-5, c=1

The quadratic formula is given by

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

We substitute the values to get,

x =  \frac{ -  - 5 \pm \sqrt{ {( - 5)}^{2}  - 4(1)(2)} }{2(2)}

x =  \frac{ 5 \pm \sqrt{ 17} }{4}

x = \frac{5}{4}   -  \frac{  \sqrt{ 17} }{4}

or

x = \frac{5}{4}   +  \frac{  \sqrt{ 17} }{4}

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