Applying equation of the second degree we have that
A=5
B=7
C=2
Solving the quadratic equation it gives us as result that has two real solutions
X1 =-1
X2 =-2/5
The number of solutions of the equation [tex]5{x^2} + 7x +2[/tex] is [tex]\boxed2[/tex] and the solutions of the equation is [tex]\boxed{x = - 1}[/tex] and [tex]\boxed{x = - \frac{2}{5}}.[/tex]
Further explanation:
Given:
The equation is [tex]f\left( x \right) = 5{x^2} + 7x +2.[/tex]
Explanation:
The polynomial has n roots if the degree of the polynomial is n.
[tex]f\left( x \right) = a{x^n} + b{x^{n - 1}} + \ldots+ cx + d[/tex]
The given equation is [tex]f\left( x \right) = 5{x^2} + 7x +2.[/tex]
Equation has 2 zeros or solutions as the equation is quadratic.
Solve the above equation to obtain the zeros.
[tex]\begin{aligned}5{x^2} + 7x + 2 &= 0\\5{x^2} + 5x + 2x + 2 &= 0 \\ 5x\left( {x + 1} \right) + 2\left( {x + 1} \right) &= 0\\\left( {5x + 2} \right)\left( {x + 1} \right) &= 0\\\left( {5x + 2} \right) &= 0{\text{ or}}\;x + 1 &= 0 \\ x &= - \frac{2}{5}{\text{ or }}x &= - 1 \\\end{aligned}[/tex]
The number of solutions of the equation [tex]5{x^2} + 7x +2[/tex] is [tex]\boxed2[/tex] and the solutions of the equation is [tex]\boxed{x = - 1}[/tex] and [tex]\boxed{x = -\frac{2}{5}}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Polynomial
Keywords: solutions, number of solutions, 0, 1, 2, 3, roots, linear equation, quadratic equation, zeros, function, polynomial, solution, cubic function, degree of the function, multiplicity of 1, multiplicity of 2.
