Is the following situation possible? If so,determine their present ages. The sum of the ages of two friends is $20$ years. Four years ago,the product of their ages in years was $48$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(D) Let the age of one friend be $x$ years.
Age of the other friend will be $(20-x)$ years.
Four years ago,the age of the first friend was $(x-4)$ years.
The age of the second friend was $(20-x-4) = (16-x)$ years.
According to the given condition:
$(x-4)(16-x) = 48$
$16x - x^2 - 64 + 4x = 48$
$-x^2 + 20x - 64 = 48$
$-x^2 + 20x - 112 = 0$
$x^2 - 20x + 112 = 0$
Comparing this equation with the standard form $ax^2 + bx + c = 0$,we get $a=1, b=-20, c=112$.
The discriminant $D = b^2 - 4ac = (-20)^2 - 4(1)(112) = 400 - 448 = -48$.
Since the discriminant $D < 0$,there are no real roots for this quadratic equation.
Therefore,the given situation is not possible.

Explore More

Similar Questions

Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $2x^2 - 2\sqrt{2}x + 1 = 0$.

Find two consecutive positive integers,the sum of whose squares is $365$.

Represent the following situation in the form of a quadratic equation:
Rohan's mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohan's present age.

Represent the following situation in the form of a quadratic equation:
The product of two consecutive positive integers is $306$. We need to find the integers.

Check whether the following is a quadratic equation:
$x^{2}+3x+1=(x-2)^{2}$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo