# CBSE Class 10-Mathematics: Chapter – 4 Quadratic Equations Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 11:

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is . If so, find its length and breadth.

Let breadth of rectangular mango grove metres

Let length of rectangular mango grove metres

According to given condition:

Comparing equation with general form of quadratic equation , we get and

Discriminant

Discriminant is greater than 0 means that equation has two disctinct real roots.

Therefore, it is possible to design a rectangular grove.

Applying quadratic formula, to solve equation,

We discard negative value of x because breadth of rectangle cannot be in negative.

Length of rectangle metres

Question 12:

Is the following situation possible? If so, determine their present ages.

The sum of the ages of two friends is years. Four years ago, the product of their ages in years was .

Let age of first friend = x years and let age of second friend years

Four years ago, age of first friend years

Four years ago, age of second friend years

According to given condition,

Comparing equation, with general quadratic equation , we get and

Discriminant

Discriminant is less than zero which means we have no real roots for this equation.

Therefore, the give situation is not possible

Question13:

Value of for is quadratic formula is

(a)

(b)

(c)

(d)

(c)

Question 14:

Discriminate of is

(a)

(b)

(c)

(d)