Respuesta :
The solutions for the given equation [tex]4x^2+x-3=0[/tex] are x = -1 and x = 3/4. Using the quadratic formula, the solutions for the given equation are calculated.
What is the quadratic formula?
The formula which is used to calculate the roots(solutions) of the quadratic equation in the form [tex]ax^2+bx+c=0[/tex] is
x = [- b ± [tex]\sqrt{b^2-4ac}[/tex]]/2a
Calculation:
The given equation is [tex]4x^2+x-3=0[/tex]
In comparison with the standard form of quadratic equation [tex]ax^2+bx+c=0[/tex],
we get, a = 4, b = 1 and c = -3
So, solving the given equation using the quadratic formula,
x = [- b ± [tex]\sqrt{b^2-4ac}[/tex]]/2a
= [- 1 ± [tex]\sqrt{1-4(4)(-3)}[/tex]]/2(4)
= [-1 ± [tex]\sqrt{49}[/tex]]/8
= (-1 ± 7)/8
Thus, x = (-1 + 7)/8 = 3/4 and x = (-1-7)/8 = -8/8 = -1
Therefore, the solutions of the given equation are x = -1 and x = 3/4.
Learn more about solving quadratic equations here:
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