NCERT Class 10 Chapter 5 Quadratic Equations Official CBSE Board Sample Problems Short Answer
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Question
If- 5 is a root of the quadratic equation and the quadratic equation has equal roots, find the value of k
Solution
is the root of the quadratic equation
Now, given that equation has equal roots
I.e. has equal roots
I.e. has equal roots
(For equal roots, D = 0, i.e.]
Question
If and are roots of the quadratic equations, find the values ofaand b.
Solution
Given quadratic equation is ..(i)
(x = is the root of equation (i))
...(ii)
[ is the root of equation (i)]
..(iii)
Putting the value of b from (iii) in (ii), we get
Putting a = 3 in (iii), we have
Question
A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.
Solution
Let ones digit of number = x
Let tens digit of number = y
Number will be
According to question,
…(i)
and ...(ii)
Putting from (i) in (ii), we get,
and )
The required number .
Question
Solve for x:
Solution
Question
If the roots of the quadratic equation are equal, prove that.
Solution
For equal roots, discriminant, D = 0
Question
The following picture shows the shape of a certain grass patch. If the area of the patch is , find k.

The Shape of a Certain Grass Patch
Solution
The total area
Since the area is
Since the length cannot be negative, .
Question
Using the quadratic formula, solve the quadratic equation:
Solution
and
Question
Find 2 numbers that sum to 21 and the sum of the squares is 261.
Solution
The numbers are 15 and 6.
Hence,and
Question
Find the roots of the following equations:
Solution
On simplifying we get
Question
If p and q are the roots of the equation , then find the value of p and q.
Solution
Since p and q are the roots of this equation, Hence:. Hence,
Hence,
Question
Find the value of k for which the quadratic equation has two real and equal roots.
Solution
For equal roots