Question

How do you solve $ {x^2} + 2x - 48 = 0 $ ?

Answer 1

Hint: An expression that contains numerical values and alphabets representing the unknown variable quantities is called an algebraic expression. The equation given in the question is a polynomial equation as the unknown quantities are raised to some power and the power is a non-negative integer (the numerical values written with the unknown quantity are known as coefficients); more specifically, the equation is quadratic, a quadratic equation is a type of polynomial equation.

Complete step-by-step answer:
As the equation is of degree two, it can be solved by any of the methods like factorization, completing the square, quadratic formula, etc. Using the appropriate method, we can find out the correct answer.
The given equation is $ {x^2} + 2x - 48 = 0 $
It can be solved by factorization as well as –
 $
  {x^2} + 2x - 48 = 0 \\
  {x^2} + 8x - 6x - 48 = 0 \\
   \Rightarrow x(x + 8) - 6(x + 8) = 0 \\
   \Rightarrow (x + 8)(x - 6) = 0 \\
   \Rightarrow x = - 8,\,x = 6 \;
  $
Hence, the factors of the equation are $ x + 8 = 0 $ and $ x - 6 = 0 $ .
So, the correct answer is “ $ x + 8 = 0 $ and $ x - 6 = 0 $ ”.

Note: The roots of an equation are defined as the values of the unknown variable at which the function comes out to be zero, the value of y is zero at the x-axis so the roots of an equation are simply the x-intercepts. We have to first convert the given equation in the standard equation form that is $ a{x^2} + bx + c = 0 $ to solve the equation further by factorization. Comparing the given equation with the standard equation, we find the values of a, b and c. The condition for factorization is, $ {b_1} \times {b_2} = a \times c $ . We find the value of $ {b_1} $ and $ {b_2} $ by hit and trial. We use the quadratic formula if we are not able to solve an equation by factorization.