Answer

Verified

340.8k+ views

**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.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Write the difference between soap and detergent class 10 chemistry CBSE

Give 10 examples of unisexual and bisexual flowers

Differentiate between calcination and roasting class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE

a Why did Mendel choose pea plants for his experiments class 10 biology CBSE