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

Which of the following equations has the sum of its roots as $3$?

If the following quadratic equation has two equal and real roots,then find the value of $k$: $(k+1) x^{2}-2(k+3) x+(2 k+3)=0$

Difficult
View Solution

If one root of a quadratic equation $ax^2 + bx + c = 0$ is $\frac{-b + \sqrt{D}}{2a}$,then the other root is $\ldots \ldots \ldots \ldots$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $3x^{2} - 18x + k = 0$.

State whether the quadratic equation $2 x^{2}+x-1=0$ has two distinct real roots. Justify your answer.

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