Question

Найдите нули функции у=5х^2-4х-1. Пожалуйста помогите

Answer 1

1. у=5х^2 - 4х - 1

y=0

5х^2 - 4х - 1=0

D=(-4)^2-4*5*(-1)=16+20=36

x1=(4+6)/10=1

x2=(4-6)/10=-1/5

A(1;0); B(-1/5;0)

x=0

y=-1

C(0;-1)

Answer 2

Finding the Zeros of the Function

To find the zeros of the function \( y = 5x^2 - 4x - 1 \), we can use the quadratic formula, which states that for a quadratic equation of the form \( ax^2 + bx + c = 0 \), the solutions for \( x \) are given by:

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

In this case, the coefficients are: - \( a = 5 \) - \( b = -4 \) - \( c = -1 \)

Applying the Quadratic Formula

Using the quadratic formula, we can calculate the zeros of the function:

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

Solving for \( x \), we get:

\[ x = \frac{{4 \pm \sqrt{{16 + 20}}}}{{10}} \] \[ x = \frac{{4 \pm \sqrt{{36}}}}{{10}} \] \[ x = \frac{{4 \pm 6}}{{10}} \]

So, the solutions for \( x \) are:

\[ x_1 = \frac{{4 + 6}}{{10}} = \frac{{10}}{{10}} = 1 \] \[ x_2 = \frac{{4 - 6}}{{10}} = \frac{{-2}}{{10}} = -0.2 \]

Conclusion

Therefore, the zeros of the function \( y = 5x^2 - 4x - 1 \) are \( x = 1 \) and \( x = -0.2 \).