Question

How do you solve $ {x^2} = 16 $ using the quadratic formula?

Answer 1

Hint: A quadratic equation is a polynomial of degree two and the values of the unknown variable for which the value of the function comes out to be zero are called the zeros/factors/solutions of the polynomial equation, factorization, completing the square, graphs, quadratic formula, etc. are some of the methods for finding the factors of a polynomial. We have to solve the quadratic equation given in the question using the quadratic formula, so for that we will rewrite the equation and compare it to the standard equation form and then we will plug in the values of the coefficients in the quadratic formula.

Complete step-by-step answer:
The equation given is $ {x^2} = 16 $
It can be rewritten as $ {x^2} - 16 = 0 $
On comparing the given equation with the standard quadratic equation $ a{x^2} + bx + c = 0 $ , we get –
 $ a = 1,\,b = 0,\,c = - 16 $
The Quadratic formula is given as –
 $ x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} $
Putting the values in the above equation, we get –
 $
  x = \dfrac{{ - 0 \pm \sqrt {{0^2} - 4(1)( - 16)} }}{{2(1)}} \\
   \Rightarrow x = \pm \dfrac{{\sqrt {64} }}{2} \\
   \Rightarrow x = \pm \dfrac{8}{2} \\
   \Rightarrow x = \pm 4 \;
  $
Hence the zeros of the given equation are $ 4 $ and $ - 4 $ .
So, the correct answer is “ $ 4 $ and $ - 4 $ ”.

Note: An algebraic expression contains numerical values along with alphabets, a polynomial equation is obtained when the alphabets representing an unknown variable quantity are raised to some power such that the exponent is a non-negative integer. The degree of a polynomial equation is the highest exponent of the polynomial. The roots of an equation are simply the x-intercepts as on the x-axis, value of y is zero. When we fail to find the factors of the equation, we use the quadratic formula.