Answer :
To find the zeros of the quadratic function [tex]\( f(x) = 1.1x^2 + 13x + 35.8 \)[/tex], we can use the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are:
- [tex]\( a = 1.1 \)[/tex]
- [tex]\( b = 13 \)[/tex]
- [tex]\( c = 35.8 \)[/tex]
First, we calculate the discriminant [tex]\( \Delta \)[/tex]:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
[tex]\[ \Delta = 13^2 - 4(1.1)(35.8) \][/tex]
[tex]\[ \Delta = 169 - 157.6 \][/tex]
[tex]\[ \Delta = 11.4 \][/tex]
Since the discriminant is positive, there are two real roots. Now we can find the roots using the quadratic formula:
[tex]\[ x_1 = \frac{-b + \sqrt{\Delta}}{2a} \][/tex]
[tex]\[ x_1 = \frac{-13 + \sqrt{11.4}}{2 \cdot 1.1} \][/tex]
[tex]\[ x_2 = \frac{-b - \sqrt{\Delta}}{2a} \][/tex]
[tex]\[ x_2 = \frac{-13 - \sqrt{11.4}}{2 \cdot 1.1} \][/tex]
Calculating [tex]\( x_1 \)[/tex]:
[tex]\[ x_1 = \frac{-13 + 3.376}{2.2} \][/tex]
[tex]\[ x_1 = \frac{-9.624}{2.2} \][/tex]
[tex]\[ x_1 \approx -4.369 \][/tex]
Calculating [tex]\( x_2 \)[/tex]:
[tex]\[ x_2 = \frac{-13 - 3.376}{2.2} \][/tex]
[tex]\[ x_2 = \frac{-16.376}{2.2} \][/tex]
[tex]\[ x_2 \approx -7.449 \][/tex]
So, the zeros of the function [tex]\( f(x) = 1.1x^2 + 13x + 35.8 \)[/tex] are approximately:
[tex]\[ x_1 \approx -4.369 \][/tex]
[tex]\[ x_2 \approx -7.449 \][/tex]
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are:
- [tex]\( a = 1.1 \)[/tex]
- [tex]\( b = 13 \)[/tex]
- [tex]\( c = 35.8 \)[/tex]
First, we calculate the discriminant [tex]\( \Delta \)[/tex]:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
[tex]\[ \Delta = 13^2 - 4(1.1)(35.8) \][/tex]
[tex]\[ \Delta = 169 - 157.6 \][/tex]
[tex]\[ \Delta = 11.4 \][/tex]
Since the discriminant is positive, there are two real roots. Now we can find the roots using the quadratic formula:
[tex]\[ x_1 = \frac{-b + \sqrt{\Delta}}{2a} \][/tex]
[tex]\[ x_1 = \frac{-13 + \sqrt{11.4}}{2 \cdot 1.1} \][/tex]
[tex]\[ x_2 = \frac{-b - \sqrt{\Delta}}{2a} \][/tex]
[tex]\[ x_2 = \frac{-13 - \sqrt{11.4}}{2 \cdot 1.1} \][/tex]
Calculating [tex]\( x_1 \)[/tex]:
[tex]\[ x_1 = \frac{-13 + 3.376}{2.2} \][/tex]
[tex]\[ x_1 = \frac{-9.624}{2.2} \][/tex]
[tex]\[ x_1 \approx -4.369 \][/tex]
Calculating [tex]\( x_2 \)[/tex]:
[tex]\[ x_2 = \frac{-13 - 3.376}{2.2} \][/tex]
[tex]\[ x_2 = \frac{-16.376}{2.2} \][/tex]
[tex]\[ x_2 \approx -7.449 \][/tex]
So, the zeros of the function [tex]\( f(x) = 1.1x^2 + 13x + 35.8 \)[/tex] are approximately:
[tex]\[ x_1 \approx -4.369 \][/tex]
[tex]\[ x_2 \approx -7.449 \][/tex]
