Question

How do you solve ${x^2} - 9x - 10 = 0$?

Answer 1

Hint:
According to the question we have to determine the solution of the given quadratic expression which is ${x^2} - 9x - 10 = 0$. So, first of all to determine the solution or we can say that to determine the roots of the given quadratic expression we have to determine the coefficient of ${x^2}$ and the constant term.
Now, with the help of the coefficient of ${x^2}$ and the constant term we have to determine the coefficient of x by finding the factors of the product of ${x^2}$ and the constant term.
Now, have to take the terms common which can be taken as the common term in the expression obtained.

Complete step by step solution:
Step 1: First of all to determine the solution or we can say that to determine the roots of the given quadratic expression we have to determine the coefficient of ${x^2}$and the constant term. Hence,
Coefficient of ${x^2}$= 1 and the constant term = -10
Step 2: Now, with the help of coefficient of ${x^2}$and the constant term we have to determine the coefficient of x by finding the factors of the product of ${x^2}$and the constant term. Hence,
$ \Rightarrow {x^2} - (10 - 1)x - 10 = 0$
On solving the expression as obtained just above,
$ \Rightarrow {x^2} - 10x + x - 10 = 0$
Step 3: Now, have to take the terms common which can be taken as the common term in the expression obtained. Hence,
$
   \Rightarrow x(x - 10) + 1(x - 10) = 0 \\
   \Rightarrow (x + 1)(x - 10) = 0 \\
 $
Step 4: Now, as we have obtained the factors in the solution step 3 so, we can easily determine the roots/zeros of the given quadratic expression. Hence,
$
   \Rightarrow (x + 1) = 0 \\
   \Rightarrow x = - 1 \\
 $
And,
$
   \Rightarrow (x - 10) = 0 \\
   \Rightarrow x = 10 \\
 $
Final solution: Hence, we have determined the roots/zeros of the given quadratic expression which are $x = - 1$and$x = 10$.


Note:
1) It is necessary that we have to determine the coefficient of x with the help of the product of the coefficient of ${x^2}$and the constant term.
2) On solving a quadratic expression only two possible roots/zeroes can be obtained which will satisfy the given quadratic expression mean on placing these in place of x the whole expression becomes 0.