Question

verify the quadratic equation
$5 {x}^{2} - 6x - 2 = 0$
where
$x = \frac{3 + \sqrt{19} }{5}$
​

Answer 1

Answer:

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Class 10

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>>Quadratic Equations

>>Solutions of Quadratic Equations

>>Solve the quadratic equation 5x^2 - 6x -

Question

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Solve the quadratic equation 5x

2

−6x−2=0 by completing the square.

Medium

Solution

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Given quadratic equation is 5x

2

−6x−2=0.

→x

2

−

5

6

x−

5

2

=0 (Divide on both sides by 5)

→x

2

−2(

5

3

)x+

25

9

=

25

9

+

5

2

(add (

5

3

)

2

=

25

9

on both sides)

→(x−

5

3

)

2

=

25

19

→x−

5

3

=±

25

19

(take square root on both sides)

Thus, we have x=

5

3

±

5

19

=

5

3±

19

.

Hence, the solution set is {

5

3+

19

,

5

3−

19

}.