Question

How do you solve \[{x^2} - 15 = 0\]?

Answer 1

Hint: The given equation is a quadratic equation, to solve this question we should know what polynomial and quadratic equations are. An algorithmic function contacting the numerical values as the coefficient of the unknown variable raised to some power is called a polynomial. The highest exponent in a polynomial equation is known as the degree of the polynomial. A polynomial of degree two is called a quadratic polynomial and a polynomial equation has as many roots as its degree so the given equation will have two roots as it is a quadratic equation.

Complete step-by-step answer:
We have \[{x^2} - 15 = 0\].
Adding 15 on both sides of the equations, we have:
 \[ \Rightarrow {x^2} = 15\]
Taking square root on both sides we have,
 \[ \Rightarrow \sqrt {{x^2}} = \pm \sqrt {15} \]
We know square and square root will cancels out, we have
 \[ \Rightarrow x = \pm \sqrt {15} \].
Since the degree of the given polynomial is 2. Hence we have two roots.
Thus \[ \Rightarrow x = + \sqrt {15} \] and \[x = - \sqrt {15} \].
So, the correct answer is “ \[ x = + \sqrt {15} \] and \[x = - \sqrt {15} \]”.

Note: The standard form of a quadratic polynomial is \[a{x^2} + bx + c = 0\] , we find the roots of this form of equations using factoring or completing the square method or the quadratic formula. But in this question, we have a quadratic equation of the form \[a{x^2} + c = 0\] that is the value of b is equal to zero that’s why we simply bring c to the other side of the equal to sign and divide both sides by a, then square rooting both the sides of the equation we get the roots. If we have a negative number while taking root it will become an imaginary number.