CBSE Class 10-Mathematics: Chapter – 4 Quadratic Equations Part 18 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 6:

Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Answer:

Let time taken by tap of smaller diameter to fill the tank hours

Let time taken by tap of larger diameter to fill the tank hours

It means that tap of smaller diameter fills part of tank in 1 hour. … (1)

And tap of larger diameter fills part of tank in 1 hour. … (2)

When two taps are used together, they fill tank in hours.

In 1 hour, they fill part of tank

From (1) , (2) and (3) ,

Comparing equation with general equation ,

We get and

Applying quadratic formula

Time taken by larger hours

Time cannot be in negative. Therefore, we ignore this value.

Time taken by larger hours

Therefore, time taken by larger tap is hours and time taken by smaller tap is hours.

Question 7:

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.

(i)

(ii)

(iii)

Answer:

(i)

Comparing this equation with general equation ,

We get and

Discriminant

Discriminant is less than 0 which means equation has no real roots.

(ii)

Comparing this equation with general equation ,

We get

Discriminant

Discriminant is equal to zero which means equations has equal real roots.

Applying quadratic to find roots,

Because, equation has two equal roots, it means

(iii)

Comparing equation with general equation ,

We get

Discriminant

Value of discriminant is greater than zero.

Therefore, equation has distinct and real roots.

Applying quadratic formula to find roots,