Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the age of one friend be x years.
Then the age of the other friend will be (20 - x) years.
4 years ago,
Age of 1st friend = (x - 4) years
Age of 2nd friend = (20 - x - 4) = (16 - x) years
According to the question,
(x - 4) (16 - x) = 48
16x - x2 - 64 + 4x = 48
- x2 + 20x - 112 = 0
x2 - 20x + 112 = 0
Comparing this equation with ax2 + bx + c = 0, we get
a = 1, b = -20 and c = 112
Discriminant = b2 - 4ac = (-20)2 - 4 × 112
= 400 - 448
= -48
b2 - 4ac < 0
Therefore, there will be no real solution possible for the equations. Such type of condition doesn't exist.
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Solve the following quadratic equation using formula method only
`"x"^2 - 4 sqrt 15 "x" - 4 = 0`
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
If a = 1, b = 4, c = –5, then find the value of b2 – 4ac.
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case.
The quadratic equation whose roots are 1:
α and β are the roots of 4x2 + 3x + 7 = 0, then the value of `1/α + 1/β` is:
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
If –5 is a root of the quadratic equation 2x2 + px – 15 = 0, then:
Which of the following equations has the sum of its roots as 3?
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
