Question

How do you use quadratic formula to find the zeros of a function?

Answer 1

Hint: Quadratic formula can be used to find the zeros of a function given that the function consists of quadratic polynomial or an expression reducible to a quadratic polynomial. A polynomial of degree two is called a quadratic polynomial and its zeros can be found using many methods like factorization, completing the square, graphs, quadratic formula etc.

Complete step-by-step answer:
The quadratic formula is used when we fail to find the factors of the equation by any other method. In the given question, we have to solve the given quadratic equation using the quadratic formula. So for that, we will have to first bring the given equation in the standard equation form and then plug in the values of the coefficients in the quadratic formula.
The given question requires us to find the zeros of a function using quadratic formula.
Let the function consist of a quadratic polynomial $ \left( {a{x^2} + bx + c} \right) $ .
Now, we can find the zeros of the function by plugging in the values of coefficients of the terms.
The Quadratic formula is given as:
 $ x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} $
Hence the zeros of the given function can be found easily using the quadratic formula

Note: A polynomial equation is an algebraic expression that contains numerical values and alphabets too, but when the alphabets representing an unknown variable quantity are raised to some power such that the exponent is a non-negative integer, the algebraic expression becomes a polynomial equation. The highest exponent of the polynomial in a polynomial equation is called its degree. Now, various fields of mathematics require the point at which the value of a polynomial is zero, those values are called the factors/solution/zeros of the given polynomial. On the x-axis, the value of y is zero so the roots of an equation are the points on the x-axis, that is the roots are simply the x-intercepts.