Question

How do you solve the equation \[5{{y}^{2}}=30y\] ?

Answer 1

Hint: Take all the terms to the L.H.S. Divide both sides with 5 to simplify the equation. Now, take y common from the two terms and factorize the expression. Substitute each term equal to 0 and find the two values of y to get the answer.

Complete step by step solution:
Here we have been provided with the quadratic equation \[5{{y}^{2}}=30y\] and we are asked to solve it. That means we have to find the two values of y also known as the roots of the quadratic equation.
Let us use the factorization method to solve the question. But first we need to take all the terms to the L.H.S, so we get,
\[\Rightarrow 5{{y}^{2}}-30y=0\]
Since 5 is a constant so we can divide both the sides with 5 to simplify the equation,
\[\Rightarrow {{y}^{2}}-6y=0\]
Now, taking the variable y common from the two terms we get the factored form of this equation:
\[\Rightarrow y\left( y-6 \right)=0\]
Substituting each term equal to 0 we get,
\[\Rightarrow y = 0\] or $(y – 6) = 0$
\[\therefore y = 0\] or $y = 6$
Hence, the two roots of the given quadratic equation are: y = 0 or 6.

Note: You may note that this was a quadratic equation and that is why we must have obtained two roots. Here, you must not divide both the sides with the variable y otherwise one root, i.e. y = 0 would vanish and we will get only one root. In that case our answer will be considered incomplete. Here the constant term was 0 otherwise we would have used the middle term split method to get the roots.