Question

How many real solutions are there for 5x^2+7x+2?

Answer 1

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

Answer 2

The number of solutions of the equation $5{x^2} + 7x +2$ is $\boxed2$ and the solutions of the equation is $\boxed{x = - 1}$ and $\boxed{x = - \frac{2}{5}}.$

Further explanation:

Given:

The equation is $f\left( x \right) = 5{x^2} + 7x +2.$

Explanation:

The polynomial has n roots if the degree of the polynomial is n.

$f\left( x \right) = a{x^n} + b{x^{n - 1}} + \ldots+ cx + d$

The given equation is $f\left( x \right) = 5{x^2} + 7x +2.$

Equation has 2 zeros or solutions as the equation is quadratic.

Solve the above equation to obtain the zeros.

$\begin{aligned}5{x^2} + 7x + 2 &= 0\\5{x^2} + 5x + 2x + 2 &= 0 \\ 5x\left( {x + 1} \right) + 2\left( {x + 1} \right) &= 0\\\left( {5x + 2} \right)\left( {x + 1} \right) &= 0\\\left( {5x + 2} \right) &= 0{\text{ or}}\;x + 1 &= 0 \\ x &= - \frac{2}{5}{\text{ or }}x &= - 1 \\\end{aligned}$

The number of solutions of the equation $5{x^2} + 7x +2$ is $\boxed2$ and the solutions of the equation is $\boxed{x = - 1}$ and $\boxed{x = -\frac{2}{5}}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497.

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.