QUADRATIC EQUATIONS
Hence the situation is not possible.
1
) years
- 4
On comparing with ax2 + bx + c = 0,
2. 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.
Sol.
Let first friend's age
=
x years
∴
Second friend's age
=
(20 - x) years
∴
Four years ago,
First friend's age
=
(x - 4) years
Second friend's age
=
(20 - x
According to the given condition,
(x - 4)
=
48
∴
16x - x2 - 64 + 4x
=
48
∴
- x2 + 20x - 64 - 48
=
0
∴
- x2 + 20x - 112
=
0
∴
x2 - 20x + 112
=
0
Do we know their ages ?
No
∴ 2nd Friend’s age = 20 - x
=
(16 - x) years
∴
a = 1,
b = - 20,
c = 112,
b2 - 4ac
=
(- 20)2 - 4 × 1 × 112
=
400 - 448
=
- 48
=
∴
b2 - 4ac
- 48 < 0
The equation has no real roots.
∴
What we need to find ?
Product means multiplication
Calculation
112
56
28
2
2
2
14
2
7
7
1
7 + 16
≠
20
14 + 8
≠
20
Since it is not possible to factorise the equation.
Let us use the formula method
Let us do the prime factorization of 112
(16 - x)
1st Friend’s age + 2nd Friend’s age = 20
x + 2nd Friend’s age = 20
We don’t get two factors in such a way that by adding we get middle number 20
EX 4.4 4