The sum of the numbers is 15 and the sum of their reciprocals is 3 10 . Formulate the quadratic equation to find the two numbers.

Let the two numbers be x and 15 - x . Now, reciprocals of x and 15 - x are 1 x and 1 15 - x respectively. Then, sum of their reciprocals = 1 x + 1 15 - x Given, sum of their reciprocals = 3 10 ∴ 1 x + 1 15 - x = 3 10 Taking LCM of the denominators in LHS, we get ⇒ 15 - x + x x 15 - x = 3 10 ⇒ 15 15 x - x 2 = 3 10 ⇒ 5 15 x - x 2 = 1 10 Transposing denominators, we get ⇒ 15 x - x 2 = 50 ⇒ 15 x - x 2 - 50 = 0 ⇒ x 2 - 15 x + 50 = 0 which is the required quadratic equation. Note: The answer given in the textbook seems to be wrong.

E M B I B E

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE>Q 1

EASY

10th CBSE

IMPORTANT

Earn 100

The product of two consecutive positive integers is $240$ . Formulate the quadratic equation whose roots are these integers.

Important Questions on Quadratic Equations

EASY

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE>Q 2

The sum of the square of two consecutive numbers is

390

. Formulate the quadratic equation to find the two numbers.

EASY

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE>Q 3

The sum of the numbers is

15

and the sum of their reciprocals is

\frac{3}{10}

. Formulate the quadratic equation to find the two numbers.

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE>Q 4

The product of Anil's age (in years)

3

years ago and his age (in years)

7

years later is

56

. Formulate a quadratic equation to find his present age

x

.

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE>Q 5

The height of a right-angle triangle is $7 cm$ less than its base. If the hypotenuse is $13 cm$ . Formulate the quadratic equation to find the base of the triangle.

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 4 - Quadratic Equations>EXERCISE>Q 6

The length of a park is