Question

F(x)=X^2+7x+10\x-3 Nayti nuli funkciy

Answer 1

f(x)=X^2+7x+10\x-3

D= 49-4*10

D=49-40=9

D=3^2 (три в квадрате)

Х1=3+1/2=2

Х2=3-1/2=1

 вот и все=)

Answer 2

To find the roots (zeros) of the function $f(x) = x^2 + 7x + \frac{10}{x-3}$, you need to set the function equal to zero and solve for $x$. Here's how you can do it:

$f(x) = x^2 + 7x + \frac{10}{x-3}$

Set $f(x)$ equal to zero:

$x^2 + 7x + \frac{10}{x-3} = 0$

First, let's get rid of the fraction by multiplying both sides by $(x - 3)$ to clear the fraction:

$(x - 3)(x^2 + 7x + \frac{10}{x-3}) = 0 \cdot (x - 3)$

This simplifies to:

$x(x - 3) + 7(x - 3) + 10 = 0$

Now, distribute and combine like terms:

$x^2 - 3x + 7x - 21 + 10 = 0$

Combine the $x$ terms and constants:

$x^2 + 4x - 11 = 0$

Now, you have a quadratic equation. You can solve it using the quadratic formula:

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

In this equation, $a = 1$, $b = 4$, and $c = -11$. Plug these values into the quadratic formula:

$x = \frac{-4 \pm \sqrt{4^2 - 4 \cdot 1 \cdot (-11)}}{2 \cdot 1}$

Now, calculate the values:

$x = \frac{-4 \pm \sqrt{16 + 44}}{2}$

$x = \frac{-4 \pm \sqrt{60}}{2}$

Simplify the square root:

$x = \frac{-4 \pm 2\sqrt{15}}{2}$

Now, you can simplify further by canceling the common factor of 2:

$x = -2 \pm \sqrt{15}$

So, the roots of the function $f(x)$ are $x = -2 + \sqrt{15}$ and $x = -2 - \sqrt{15}$.