Check sibling questions

A train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance if its speed were 5 km/hour more. Find the original speed of the train.

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/

A train travelling at a uniform speed for 360 km would have taken 48

Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 2
Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 3 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 4 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 5 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 6 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 7 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 8 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 9 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 10 Question 23 - CBSE Class 10 Sample Paper for 2018 Boards - Part 11

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

Question 23 Check whether the equation 5x2 6x 2 = 0 has real roots and if it has, find them by the method of completing the square. Also verify that roots obtained satisfy the given equation. 5x2 6x 2 = 0 Comparing equation with ax2 + bx + c = 0 a = 5 , b = 6, c = 2 We know that , D = b2 4ac = ( 6)2 4 5 ( 2) = 36 + 40 = 76 Since D > 0 Hence, there are two real roots Finding roots by completing the square 5x2 6x 2 = 0 Dividing by 5 (5 2 6 2)/5=0/5 5 2/5 6 /5 2/5=0 x2 6 /5 2/5=0 We know that (a b)2 = a2 2ab + b2 Here, a = x & 2ab = 6 /5 2xb = 6 /5 b = ( 6 )/5 1/( 2 ) b = 3/5 Now, in our equation x2 6 /5 2/5=0 Adding and subtracting (3/5)^2 x2 6 /5 2/5+(3/5)^2 (3/5)^2=0 x2 6 /5+(3/5)^2 2/5 (3/5)^2=0 ( 3/5)^2 2/5 (3/5)^2=0 ( 3/5)^2 2/5 9/25=0 ( 3/5)^2=2/5+9/25 ( 3/5)^2=(2 5 + 9)/25 ( 3/5)^2=(10 + 9)/25 ( 3/5)^2=19/25 ( 3/5)^2=( 19/5)^2 Cancelling square both sides ( 3/5)= ( 19/5) x 3/5 = 19/5 x = 19/5+3/5 x = ( 19 + 3)/5 x 3/5 = ( 19)/5 x = ( 19)/5+3/5 x = ( 19 + 3)/5 Now, we will verify zeroes Verifying x = ( + )/ 5x2 6x 2 = 0 5(( 19 + 3)/5)^2 6(( 19 + 3)/5) 2=0 5((( 19 )^2+ 3^(2 )+2 3 19)/25) 6(( 19 + 3)/5) 2=0 (19 + 9 + 6 19)/5 ((6 19 +18)/5) 2=0 (28 + 6 19 6 19 18 2(5))/5=0 (28 18 10)/5=0 (28 28)/5=0 0/5=0 0 =0 Which is true Hence, ( + )/ is a root of the equation Verifying x = ( + )/ 5x2 6x 2 = 0 5(( 19 + 3)/5)^2 6(( 19 + 3)/5) 2=0 5((( 19 )^2+ 3^(2 )+ 2 3 ( 19))/25) 6(( 19 + 3)/5) 2=0 (19 + 9 6 19)/5 (( 6 19 +18)/5) 2=0 (28 6 19 + 6 19 18 2(5))/5=0 (28 18 10)/5=0 (28 28)/5=0 0/5=0 0 =0 Which is true Hence, ( + )/ is a root of the equation

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.