###### Advertisements

###### Advertisements

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John had x marbles.

###### Advertisements

#### Solution

Let the number of John's marbles be x.

Therefore, number of Jivanti's marble = 45 - x

After losing 5 marbles,

Number of John's marbles = x - 5

Number of Jivanti's marbles = 45 - x - 5 = 40 - x

It is given that the product of their marbles is 128.

∴ (x - 5)(40 - x) = 128

⇒ 40x - x^{2} – 200 + 5x = 128

⇒ 45x - x^{2} – 200 - 128 = 0

⇒ 45x - x^{2} - 328 = 0

⇒ -(x^{2} - 45 + 328) = 0

⇒ x^{2} - 45 + 328 = 0

∴ The required quadratic equation is x^{2} - 45 + 328 = 0

#### APPEARS IN

#### RELATED QUESTIONS

Find the value of a, b, c in the following quadratic equation : 2x^{2} ‒ x ‒ 3 = 0

Write the quadratic equation whose roots are ‒2 and ‒3.

If α + β = 5 and α^{3} +β^{3} = 35, find the quadratic equation whose roots are α and β.

(x + 5)(x - 2) = 0, find the roots of this quadratic equation

Write the following quadratic equation in a standard form: 3x^{2} =10x + 7.

State whether the given equation is quadratic or not. Give reason.

`5/4m^2 - 7 = 0`

Check whether the following is quadratic equation or not.

`2x^2-sqrt(3x)+9=0`

Solve x^{4} – 10x^{2} +9 =0

The area of a big rectangular room is 300 m². If the length were decreased by 5 m and the breadth increased by 5 m; the area would be unaltered. Find the length of the room.

An employer finds that if he increased the weekly wages of each worker by Rs 5 and employs five workers less, he increases his weekly wage bill from Rs 3,150 to Rs 3,250. Taking the original weekly wage of each worker as Rs x; obtain an equation in x and then solve it to find the weekly wages of each worker.

Find the value of x, if a+1=0 and `x^2 + ax – 6 = 0`

Solve each of the following equations using the formula:

`x^2 + 6x – 10 = 0`

Which of the following are quadratic equation in x?

`2x^2+5/2xsqrt3=0`

Which of the following are quadratic equation in x?

`x^2-1/x^2=5`

Which of the following are quadratic equation in x?

(2x+3)(3x+2)=6(x-1)(x-2)

`sqrt7x^2-6x-13sqrt7=0`

`4sqrt6x^2-13x-2sqrt6=0`

`2x^2+ax-a^2=0`

`1/(x+1)+2/(x+2)=5/(x+4),x≠-1,-2,-4`

`3^((x+2))+3^(-x)=10`

Solve any two of the following.

Form a quadratic equation whose roots are 4 and -12.

Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less. Find 'x'.

Find the quadratic equation, whose solution set is :

(-2,3}

Write the following quadratic equation in standard form ax^{2} + bx + c = 0 : x (x + 3) = 7

Solve the following quadratic equation by using formula method :

7y^{2} - 5y - 2 = 0

Write the quadratic equation 3y^{2 }= 10y +7 in the standard form ax^{2} + bx + c = 0 .

If x + y = 5 and x - y = 1, then find the value of x.

If `(2)/(3)` is a solution of the equation 7x^{2} + kx – 3 = 0, find the value of k.

Solve the following equation by using quadratic equations for x and give your 5x(x + 2) = 3

**Choose the correct answer from the given four options :**

If `(1)/(2)` is a root of the quadratic equation 4x^{2} – 4kx + k + 5 = 0, then the value of k is

**Choose the correct answer from the given four options :**

If one root of a quadratic equation with rational coefficients is `(3 - sqrt(5))/(2)`, then the other

From the following equations, which one is the quadratic equation?

Find the values of a and b from the quadratic equation 2x^{2} – 5x + 7 = 0.

**Choose the correct alternative answer for the following sub questions and write the correct alphabet.**

Which of the following is a quadratic equation?

Write the given quadratic equation in standard form.

m (m – 6) = 9