rohan's mother is 26 years older than him . the product of their age 3 years from now will be 360 . we would like to find rohan ' s present age quadratic or not?​

Iwan

1+4+3= i love you

sorry I dont now this question

sorry sa iba kanalang nag hanap ty

(i) Let us consider,

Breadth of the rectangular plot = x m

Thus, the length of the plot = (2x + 1) m.

As we know,

Area of rectangle = length × breadth = 528 m²

Putting the value of length and breadth of the plot in the formula, we get,

(2x + 1) × x = 528

⇒ 2x² + x =528

⇒ 2x² + x – 528 = 0

Therefore, the length and breadth of plot, satisfies the quadratic equation, 2x² + x – 528 = 0, which is the required representation of the problem mathematically.

(ii) Let us consider,

The first integer number = x

Thus, the next consecutive positive integer will be = x + 1

Product of two consecutive integers = x × (x +1) = 306

⇒ x² + x = 306

⇒ x² + x – 306 = 0

Therefore, the two integers x and x+1, satisfies the quadratic equation, x² + x – 306 = 0, which is the required representation of the problem mathematically.

(iii) Let us consider,

Age of Rohan’s = x years

Therefore, as per the given question,

Rohan’s mother’s age = x + 26

After 3 years,

Age of Rohan’s = x + 3

Age of Rohan’s mother will be = x + 26 + 3 = x + 29

The product of their ages after 3 years will be equal to 360, such that

(x + 3)(x + 29) = 360

⇒ x² + 29x + 3x + 87 = 360

⇒ x² + 32x + 87 – 360 = 0

⇒ x² + 32x – 273 = 0

Therefore, the age of Rohan and his mother, satisfies the quadratic equation, x² + 32x – 273 = 0, which is the required representation of the problem mathematically.

(iv) Let us consider,

The speed of train = x km/h

And

Time taken to travel 480 km = km/hr

As per second condition, the speed of train = (x – 8) km/h

Also given, the train will take 3 hours to cover the same distance.

Therefore, time taken to travel 480 km = km/h

As we know,

Speed × Time = Distance

Therefore,

(x – 8)= 480

⇒ 480 + 3x – – 24 = 480

⇒ 3x – = 24

⇒ 3x² – 8x – 1280 = 0

Therefore, the speed of the train, satisfies the quadratic equation, 3x² – 8x – 1280 = 0, which is the required representation of the problem mathematically.

(i) Let us consider,

Breadth of the rectangular plot = x m

Thus, the length of the plot = (2x + 1) m.

As we know,

Area of rectangle = length × breadth = 528 m²

Putting the value of length and breadth of the plot in the formula, we get,

(2x + 1) × x = 528

⇒ 2x² + x =528

⇒ 2x² + x – 528 = 0

Therefore, the length and breadth of plot, satisfies the quadratic equation, 2x² + x – 528 = 0, which is the required representation of the problem mathematically.

(ii) Let us consider,

The first integer number = x

Thus, the next consecutive positive integer will be = x + 1

Product of two consecutive integers = x × (x +1) = 306

⇒ x² + x = 306

⇒ x² + x – 306 = 0

Therefore, the two integers x and x+1, satisfies the quadratic equation, x² + x – 306 = 0, which is the required representation of the problem mathematically.

(iii) Let us consider,

Age of Rohan’s = x years

Therefore, as per the given question,

Rohan’s mother’s age = x + 26

After 3 years,

Age of Rohan’s = x + 3

Age of Rohan’s mother will be = x + 26 + 3 = x + 29

The product of their ages after 3 years will be equal to 360, such that

(x + 3)(x + 29) = 360

⇒ x² + 29x + 3x + 87 = 360

⇒ x² + 32x + 87 – 360 = 0

⇒ x² + 32x – 273 = 0

Therefore, the age of Rohan and his mother, satisfies the quadratic equation, x² + 32x – 273 = 0, which is the required representation of the problem mathematically.

(iv) Let us consider,

The speed of train = x km/h

And

Time taken to travel 480 km = \frac{480}{x}

x

480

km/hr

As per second condition, the speed of train = (x – 8) km/h

Also given, the train will take 3 hours to cover the same distance.

Therefore, time taken to travel 480 km = \frac{480}{(x+3)}

(x+3)

480

km/h

As we know,

Speed × Time = Distance

Therefore,

(x – 8)\frac{(480}{(x + 3)}

(x+3)

(480

= 480

⇒ 480 + 3x – \frac{3840}{x}

x

3840

– 24 = 480

⇒ 3x – \frac{3840}{x}

x

3840

= 24

⇒ 3x² – 8x – 1280 = 0

Therefore, the speed of the train, satisfies the quadratic equation, 3x² – 8x – 1280 = 0, which is the required representation of the problem mathematically.