Name: Nature of the Roots: Illustration
Uploaded: 2019-07-19
Duration: 2 min 4 s
Description: We cannot judge a book by its cover, but we can find the nature of the roots of a given quadratic equation without finding roots. Let's learn just how we can...

Question

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

.

Accepted Answer

Let the age of one friend be $x$ years.

Age of the other friend will be $= (20 - x)$ years.

Four years ago, age of $1^{s t}$ friend $= (x - 4)$ years

and, age of $2^{n d}$ friend $= ((20 - x) - 4) = (16 - x)$ years

As per the question,

$(x - 4) (16 - x) = 48$

$16 x - 64 - x^{2} + 4 x = 48$

$- x^{2} + 20 x - 112 = 0$

$x^{2} - 20 x + 112 = 0$

Comparing this equation with $a x^{2} + b x + c = 0$ , we obtain

$a = 1, b = - 20, c = 112$

Discriminant $= b^{2} - 4 a c = {(- 20)}^{2} - 4 (1) (112)$

$= 400 - 448 = - 48$

As $b^{2} - 4 a c < 0$ ,

Thus, no real roots are possible for this equation and hence, this situation is not possible.

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 $48$ .

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

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.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

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 $48$ .