# CBSE Class 10-Mathematics: Chapter – 4 Quadratic Equations Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 9**:

A train travels at a uniform speed. If, the speed had been more, it would have taken hour less for the same journey. Find the speed of the train.

**Answer**:

Let the speed of the train

If, speed had been more, train would have taken hour less.

So, according to this condition

Comparing equation with general equation ,

We get and

Applying quadratic formula

Since speed of train cannot be in negative. Therefore, we discard

Therefore, speed of train

**Question 10**:

Find the value of for each of the following quadratic equations, so that they have two equal roots.

(i)

(ii)

**Answer**:

(i)

We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero.

Comparing equation with general quadratic equation , we get , and

Discriminant

Putting discriminant equal to zero

(ii)

Comparing quadratic equation with general form , we get , and

Discriminant

We know that two roots of quadratic equation are equal only if discriminant is equal to zero.

Putting discriminant equal to zero

The basic definition of quadratic equation says that quadratic equation is the equation of the form , where .

Therefore, in equation , we cannot have .

Therefore, we discard .

Hence the answer is .