Answer :
To find the zeros of the function [tex]\( y = 2x^2 + 9x + 4 \)[/tex], we'll use a method called the quadratic formula. This formula is used to find the roots of a quadratic equation of the form [tex]\( ax^2 + bx + c = 0 \)[/tex]. The quadratic formula is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
For the function [tex]\( y = 2x^2 + 9x + 4 \)[/tex], the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 9 \)[/tex]
- [tex]\( c = 4 \)[/tex]
First, we calculate the discriminant, which is [tex]\( b^2 - 4ac \)[/tex]:
[tex]\[ b^2 = 9^2 = 81 \][/tex]
[tex]\[ 4ac = 4 \times 2 \times 4 = 32 \][/tex]
[tex]\[ \text{Discriminant} = b^2 - 4ac = 81 - 32 = 49 \][/tex]
Since the discriminant is positive, we have two real and distinct solutions. Now, let's calculate these solutions using the quadratic formula:
1. For the first root:
[tex]\[ x_1 = \frac{-b + \sqrt{49}}{2a} = \frac{-9 + 7}{4} = \frac{-2}{4} = -0.5 \][/tex]
2. For the second root:
[tex]\[ x_2 = \frac{-b - \sqrt{49}}{2a} = \frac{-9 - 7}{4} = \frac{-16}{4} = -4 \][/tex]
Therefore, the zeros of the function [tex]\( y = 2x^2 + 9x + 4 \)[/tex] are [tex]\( x = -0.5 \)[/tex] and [tex]\( x = -4 \)[/tex].
So, the correct answer is:
A. [tex]\( x = -\frac{1}{2}, x = -4 \)[/tex]
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
For the function [tex]\( y = 2x^2 + 9x + 4 \)[/tex], the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 9 \)[/tex]
- [tex]\( c = 4 \)[/tex]
First, we calculate the discriminant, which is [tex]\( b^2 - 4ac \)[/tex]:
[tex]\[ b^2 = 9^2 = 81 \][/tex]
[tex]\[ 4ac = 4 \times 2 \times 4 = 32 \][/tex]
[tex]\[ \text{Discriminant} = b^2 - 4ac = 81 - 32 = 49 \][/tex]
Since the discriminant is positive, we have two real and distinct solutions. Now, let's calculate these solutions using the quadratic formula:
1. For the first root:
[tex]\[ x_1 = \frac{-b + \sqrt{49}}{2a} = \frac{-9 + 7}{4} = \frac{-2}{4} = -0.5 \][/tex]
2. For the second root:
[tex]\[ x_2 = \frac{-b - \sqrt{49}}{2a} = \frac{-9 - 7}{4} = \frac{-16}{4} = -4 \][/tex]
Therefore, the zeros of the function [tex]\( y = 2x^2 + 9x + 4 \)[/tex] are [tex]\( x = -0.5 \)[/tex] and [tex]\( x = -4 \)[/tex].
So, the correct answer is:
A. [tex]\( x = -\frac{1}{2}, x = -4 \)[/tex]
