Question

Solve the given quadratic equation $ {x^2} + 3x - 10 = 0 $ using quadratic formula

Answer 1

Hint: To solve this quadratic equation, we need to know the quadratic formula. After that we have to substitute the values in the formula. After substituting the value, we will get a solution for this quadratic equation. There will be two values for $ x $ .

Complete step-by-step answer:
The formula for the quadratic equation is,
 $ x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} $
Let’s consider the unknown value as $ x $ , Now the value for $ a = 1,b = 3, $ and $ c = - 10 $ , let’s substitute the values in the quadratic formula, we get,
 $
  x = \dfrac{{ - 3 \pm \sqrt {{3^2} - 4(1)( - 10)} }}{{2(1)}} \\
  x = \dfrac{{ - 3 \pm \sqrt {9 + 40} }}{2} \\
  x = \dfrac{{ - 3 \pm \sqrt {49} }}{2} \\
  x = \dfrac{{ - 3 \pm 7}}{2} \\
  x = \dfrac{{ - 3 + 7}}{2},\dfrac{{ - 3 - 7}}{2} \\
  x = \dfrac{4}{2},\dfrac{{ - 10}}{2} \;
  x = 2, - 5 \\
  $
As I said earlier, we get two values of $ x $ for this quadratic equation.
So, the correct answer is “ x = 2, - 5”.

Note: When we substitute two values of $ x $ in the given equation we get the value zero. For instance, let’s substitute $ x = 2 $ in the given equation $ {x^2} - 3x - 10 = 0 $ , we get, $ {(2)^2} + 3(2) - 10 = 0 $ . With this we can check our answers for the given equation. If we have any simple quadratic equation we can find the solution by factorization method or tree method. But for this given equation, we cannot find the solution by factoring the equation, the only solution we have to solve this type of equation is by using the quadratic formula.