Ex 4.3, 4 - Chapter 4 Class 10 Quadratic Equations

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 4.3, 4
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Let the Present age of 1st friend = x
Given that
Sum of ages of friends is 20 years
Thus,
Present age of 1st friend + Present age of 2nd friend = 20
x + Present age of 2nd friend = 20
Present age of 2nd friend = 20 – x
Four years ago
Age of 1st friend = x – 4
Age of 2nd friend = (20 – x) – 4 = 16 – x
Product of their ages 4 years ago was 48
(x – 4) (16 – x) = 48
Four years ago
Age of 1st friend = x – 4
Age of 2nd friend = (20 – x) – 4 = 16 – x
Product of their ages 4 years ago was 48
(x – 4) (16 – x) = 48
x (16 – x) – 4 (16 – x) = 48
16x – x2 – 64 + 4x = 48
16x – x2 – 64 – 14x – 48 = 0
– x2 + 16x + 4x – 64 – 48 = 0
– x2 + 20x – 112 = 0
x2 – 20x + 112 = 0
Comparing the equation with ax2 + bx + c
a = 1, b = –20, c = 112
We know that
D = b2 – 4ac
D = (–20)2 – (4 × 𝟏 × 𝟏𝟏𝟐)
D = 400 – 448
D = –48
Since D < 0
The equation has no real roots
Hence, the given situation is not possible

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!