Answer :
To construct a quadratic equation in the standard form [tex]\( ax^2 + bx + c = 0 \)[/tex] using the given values [tex]\( a = 5 \)[/tex], [tex]\( b = 3 \)[/tex], and [tex]\( c = -2 \)[/tex], let’s follow these steps:
1. Identify the standard form of a quadratic equation: [tex]\( ax^2 + bx + c = 0 \)[/tex].
2. Plug in the given values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
- [tex]\( a = 5 \)[/tex]
- [tex]\( b = 3 \)[/tex]
- [tex]\( c = -2 \)[/tex]
3. Substitute these values into the standard form:
[tex]\[ 5x^2 + 3x - 2 = 0 \][/tex]
4. Compare this equation with the given options to determine the correct match.
Let's look at the options provided:
A) [tex]\( 5x^2 + 3x - 2 = 0 \)[/tex]
B) [tex]\( 5x^2 - 3x - 2 = 0 \)[/tex]
C) [tex]\( -5x^2 + 3x + 2 = 0 \)[/tex]
D) [tex]\( -5x^2 + 3x - 2 = 0 \)[/tex]
E) [tex]\( 5x^2 + 3x + 2 = 0 \)[/tex]
From our constructed equation [tex]\( 5x^2 + 3x - 2 = 0 \)[/tex], we can see that the correct answer is:
A) [tex]\( 5x^2 + 3x - 2 = 0 \)[/tex]
1. Identify the standard form of a quadratic equation: [tex]\( ax^2 + bx + c = 0 \)[/tex].
2. Plug in the given values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
- [tex]\( a = 5 \)[/tex]
- [tex]\( b = 3 \)[/tex]
- [tex]\( c = -2 \)[/tex]
3. Substitute these values into the standard form:
[tex]\[ 5x^2 + 3x - 2 = 0 \][/tex]
4. Compare this equation with the given options to determine the correct match.
Let's look at the options provided:
A) [tex]\( 5x^2 + 3x - 2 = 0 \)[/tex]
B) [tex]\( 5x^2 - 3x - 2 = 0 \)[/tex]
C) [tex]\( -5x^2 + 3x + 2 = 0 \)[/tex]
D) [tex]\( -5x^2 + 3x - 2 = 0 \)[/tex]
E) [tex]\( 5x^2 + 3x + 2 = 0 \)[/tex]
From our constructed equation [tex]\( 5x^2 + 3x - 2 = 0 \)[/tex], we can see that the correct answer is:
A) [tex]\( 5x^2 + 3x - 2 = 0 \)[/tex]
