Question

How do you solve $5{{t}^{2}}=25t$?

Answer 1

Hint: The given equation is a quadratic equation in t. To solve the equation means we have to find the values of t that satisfy the equation. To solve a quadratic equation there are three methods. The given equation is a simple quadratic equation so you can use the method of factorisation.

Complete step-by-step solution:
The given equation is a quadratic equation in t as the degree of the equation is 2.
There are three ways to solve a quadratic equation. We shall use the method of factorisation to find the value or values of t that satisfy the given equation.
Method of factorisation is a method in which we write the equation as the product of linear polynomials which is equal to zero.
Let us first write the given equation in the standard form as $5{{t}^{2}}-25t=0$ …. (i)
We can see that the left hand side of the equation has a common multiple, i.e. 5. Therefore, we shall divide the equation (i) by 5 on both sides.
This gives us that ${{t}^{2}}-5t=0$
Now, we can see that the left hand side polynomial has a term ‘t’ in common. Therefore, we can write the equation in factored form as $t(t-5)=0$.
This means that either $t=0$ or $t-5=0$
This further means that either $t=0$ or $t=5$
Therefore, there are two values of t which satisfy the given equation. Hence, the solutions of the equation are 0 and 5.

Note: Other than factorisation, you may also use the complete square method or the quadratic formula to solve the quadratic equation. Unless it is mentioned which one to use, you can use any of the methods. Students must note that the number of solutions to a given equation in one variable is always less than or equal to the degree of the polynomial in the given equation.