Question

homework assignment 5.5 zeros of polynomials due friday by 11:59pm points 12 submitting an external tool homework assignment 5.5 zeros of polynomials score: 4/12 answered: 4/12 question 5 find all zeros of the function f(x)=4x - 20x² + 31x - 15. enter the zeros separated by commas. question help: video written example message instructor

Explanation:

Step1: Set the function equal to zero.

$4x - 20x^{2}+31x - 15=0$
Combine like - terms: $-20x^{2}+35x - 15 = 0$. Divide through by - 5 to simplify: $4x^{2}-7x + 3=0$.

Step2: Use the quadratic formula.

For a quadratic equation $ax^{2}+bx + c = 0$ ($a = 4$, $b=-7$, $c = 3$), the quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.
First, calculate the discriminant $\Delta=b^{2}-4ac=(-7)^{2}-4\times4\times3=49 - 48 = 1$.
Then, $x=\frac{7\pm\sqrt{1}}{2\times4}=\frac{7\pm1}{8}$.

Step3: Find the two solutions.

When we take the plus sign: $x=\frac{7 + 1}{8}=\frac{8}{8}=1$.
When we take the minus sign: $x=\frac{7-1}{8}=\frac{6}{8}=\frac{3}{4}$.

Answer:

$1,\frac{3}{4}$