Introduction to Linear Polynomials
• Class 9 Mathematics • Ganita Manjari
Practice Mode:
पहले question को खुद पढ़ें और solve करने की कोशिश करें।
समझ न आए तो
हिंदी में समझें
दबाएँ।
उसके बाद
Solution देखें
से step-by-step solution check करें।
Question 1
Evaluate the linear polynomial
5x − 3
for the following values:
(i)
x = 0
(ii)
x = −1
(iii)
x = 2
हिंदी में समझें:
Polynomial है:
5x − 3
हर part में x की दी हुई value को
x की जगह रखना है।
पहले x = 0,
फिर x = −1
और फिर x = 2 रखकर answer निकालेंगे।
Step-by-Step Solution:
(i) x = 0
5(0) − 3
= −3
(ii) x = −1
5(−1) − 3
= −5 − 3
= −8
(iii) x = 2
5(2) − 3
= 10 − 3
= 7
✅ Final Answers:
(i) −3
(ii) −8
(iii) 7
Question 2
Evaluate the quadratic polynomial
7s² − 4s + 6
for the following values:
(i)
s = 0
(ii)
s = −3
(iii)
s = 4
हिंदी में समझें:
हमें polynomial
7s² − 4s + 6
में हर बार दी गई s की value रखनी है।
ध्यान रखें कि पहले
s²
निकालें और फिर पूरा expression solve करें।
Salil’s mother is presently three times as old as Salil.
After 5 years, the sum of their ages will be 70 years.
Find their present ages.
हिंदी में समझें:
Salil की present age को
x years
मानते हैं।
Mother की age तीन गुना है:
Mother = 3x years
5 साल बाद:
Salil = x + 5
Mother = 3x + 5
दोनों की age का sum 70 years है।
Step-by-Step Solution:
Let Salil's present age = x years.
Mother's present age = 3x years.
After 5 years:
Salil = x + 5
Mother = 3x + 5
According to the question:
(x + 5) + (3x + 5) = 70
4x + 10 = 70
4x = 60
x = 15
Therefore:
Salil = 15 years
Mother = 3 × 15 = 45 years
✅ Answer:
Salil’s present age = 15 years
Mother’s present age = 45 years
Question 4
Two positive integers have a difference of
63 and their ratio is
2 : 5.
Find the two integers.
हिंदी में समझें:
Ratio 2 : 5 है।
इसलिए numbers को
2x
और
5x
मान सकते हैं।
दोनों numbers का difference 63 है।
इसलिए equation बनाएँगे:
5x − 2x = 63
Step-by-Step Solution:
Let the two integers be:
2x and 5x
Their difference is 63:
5x − 2x = 63
3x = 63
x = 21
Therefore:
2x = 42
5x = 105
✅ Answer:
The two integers are
42 and 105.
Question 5
Ruby has three times as many two-rupee coins
as five-rupee coins.
The total value of all these coins is
₹88.
Find the number of coins of each type.
हिंदी में समझें:
Five-rupee coins की संख्या को
x
मानते हैं।
Two-rupee coins इसकी तीन गुना हैं:
3x
अब total value:
Five-rupee coins = 5x
Two-rupee coins = 2(3x)
इन दोनों का total ₹88 है।
Step-by-Step Solution:
Let number of ₹5 coins = x.
Number of ₹2 coins = 3x.
Total value:
5x + 2(3x) = 88
5x + 6x = 88
11x = 88
x = 8
Therefore:
₹5 coins = 8
₹2 coins = 3 × 8 = 24
✅ Answer:
₹5 coins = 8
₹2 coins = 24
Question 6
A farmer cuts a
300-feet
fence into two pieces of different lengths.
The longer piece is four times the length
of the shorter piece.
Find the lengths of the two pieces.
हिंदी में समझें:
Shorter piece की length को
x feet
मानते हैं।
Longer piece = 4x feet
दोनों pieces की कुल length 300 feet है।
Step-by-Step Solution:
Let shorter piece = x feet.
Longer piece = 4x feet.