Solve the equation x - 18 x = 6 . Give your answer correct to two significant figures.

Given that: We need to solve the equation x - 18 x = 6 correct to two significant figures. We can write the equation as x 2 - 18 = 6 x ⇒ x 2 - 6 x - 18 = 0 On comparing the equation with a x 2 + b x + c = 0 , w e g e t a = 1 , b = - 6 a n d c = - 18 . On substituting the values of a,b,c in the quadratic formula, x = - b ± b 2 - 4 a c 2 a we get, x = - ( - 6 ) ± ( - 6 ) 2 - 4 ( 1 ) ( - 18 ) 2 ⇒ x = 6 ± 36 + 72 2 ⇒ x = 6 ± 108 2 ⇒ x = 6 ± 6 3 2 ⇒ x = 3 ± 3 3 Hence, the two roots can be written as, x 1 = 3 + 3 3 , x 2 = 3 - 3 3 Substituting the value of 3 = 1 . 73 , we get x 1 = 8 . 19 , x 2 = - 2 . 19 . Thus, we have the two roots of the quadratic equation correct to two significant figures as 8 . 19 and - 2 . 19

E M B I B E

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>ARCHIVES (Last 8 Years)>Q 12

MEDIUM

10th ICSE

IMPORTANT

Earn 100

Solve the following and calculate the answer correct to two decimal places.

$x^{2} - 5 x - 10 = 0$

Important Questions on Quadratic Equations in One Variable

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>ARCHIVES (Last 8 Years)>Q 13

A shopkeeper purchases a certain number of books for

₹ 960

. If the cost per book was

₹ 8

less the number of books that could be purchased for

₹ 960

, would be

4

more. Write an equation, taking the original cost of each book to be

₹ x

and solve it to find the original cost of the books.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>ARCHIVES (Last 8 Years)>Q 14

Without solving the following quadratic equation, find the value of $p$ for which the given equation has real and equal roots.

$x^{2} + (p - 3) x + p = 0$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>ARCHIVES (Last 8 Years)>Q 15

Solve the following equation and give your answer correct to three significant figures.

$5 x^{2} - 3 x - 4 = 0$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>ARCHIVES (Last 8 Years)>Q 16

Without solving the following quadratic equation, find the value of $m$ for which the given equation has real and equal roots.

$x^{2} + 2 (m - 1) x + (m + 5) = 0$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>ARCHIVES (Last 8 Years)>Q 17

A car covers a distance of $400 k m$ at a certain speed. Had the speed been $12 k m / h$ more, the time taken for the journey would have been $1 h 40 m i n$ less. Find the original speed of the car in $k m / h r$ .