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Sagot :
To solve the quadratic equation [tex]\(2x^2 + x - 4 = 0\)[/tex], we will use the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 1 \)[/tex]
- [tex]\( c = -4 \)[/tex]
Firstly, we need to calculate the discriminant, which is given by [tex]\( b^2 - 4ac \)[/tex]:
[tex]\[ \text{Discriminant} = b^2 - 4ac \][/tex]
Substituting the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[ \text{Discriminant} = 1^2 - 4 \cdot 2 \cdot (-4) \][/tex]
[tex]\[ \text{Discriminant} = 1 + 32 \][/tex]
[tex]\[ \text{Discriminant} = 33 \][/tex]
The discriminant is 33.
Now, we apply these values into the quadratic formula to find the two solutions for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{2 \cdot 2} \][/tex]
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{4} \][/tex]
This yields two solutions:
[tex]\[ x_1 = \frac{-1 + \sqrt{33}}{4} \][/tex]
[tex]\[ x_2 = \frac{-1 - \sqrt{33}}{4} \][/tex]
Approximating the values:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
So, the solutions to the quadratic equation [tex]\(2x^2 + x - 4 = 0\)[/tex] are approximately:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Here, the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 1 \)[/tex]
- [tex]\( c = -4 \)[/tex]
Firstly, we need to calculate the discriminant, which is given by [tex]\( b^2 - 4ac \)[/tex]:
[tex]\[ \text{Discriminant} = b^2 - 4ac \][/tex]
Substituting the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[ \text{Discriminant} = 1^2 - 4 \cdot 2 \cdot (-4) \][/tex]
[tex]\[ \text{Discriminant} = 1 + 32 \][/tex]
[tex]\[ \text{Discriminant} = 33 \][/tex]
The discriminant is 33.
Now, we apply these values into the quadratic formula to find the two solutions for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{2 \cdot 2} \][/tex]
[tex]\[ x = \frac{-1 \pm \sqrt{33}}{4} \][/tex]
This yields two solutions:
[tex]\[ x_1 = \frac{-1 + \sqrt{33}}{4} \][/tex]
[tex]\[ x_2 = \frac{-1 - \sqrt{33}}{4} \][/tex]
Approximating the values:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
So, the solutions to the quadratic equation [tex]\(2x^2 + x - 4 = 0\)[/tex] are approximately:
[tex]\[ x_1 \approx 1.186 \][/tex]
[tex]\[ x_2 \approx -1.686 \][/tex]
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