Quadratic Equations

page is in editing mode

🟠 (i) Area of Rectangular Plot

Given:

• Area = 528 m²

• Length = 1 more than twice the breadth

Let the breadth be x m
⇒ Length = 2x+1 m

Area = Length × Breadth

(2x+1)(x)=528⇒2x2+x=528⇒2x2+x−528=0

✅ Quadratic Equation:

2x2+x−528=0

🟠 (ii) Product of Two Consecutive Positive Integers is 306

Let the first integer be x
⇒ Next consecutive integer = x+1

Product:

x(x+1)=306⇒x2+x=306⇒x2+x−306=0

✅ Quadratic Equation:

x2+x−306=0

🟠 (iii) Age of Rohan and His Mother

Let Rohan's present age be x
⇒ Mother's age = x+26

After 3 years:

• Rohan = x+3

• Mother = x+26+3=x+29

Product of their ages:

(x+3)(x+29)=360⇒x2+32x+87=360⇒x2+32x−273=0

✅ Quadratic Equation:

x2+32x−273=0

🟠 (iv) Speed of Train Problem

Let the speed of the train be x km/h

Time = Distance ÷ Speed

• Actual time = 480x

• New speed = x−8 km/h
  ⇒ New time = 480x−8

Given:

New time=Actual time+3⇒480x−8=480x+3

Multiply through by x(x−8):

480x=480(x−8)+3x(x−8)⇒480x=480x−3840+3x2−24x⇒0=3x2−24x−3840⇒x2−8x−1280=0

✅ Quadratic Equation:

x2−8x−1280=0

Let me know if you'd like step-by-step solutions for these equations!