Advertisements
Advertisements
प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
Advertisements
उत्तर
The given quadric equation is \[2 x^2 + x + k = 0\],and roots are real.
Then find the value of k.
Here,
\[a = 2, b = 1, c = k\]
As we know that `D = b^2 - 4ac`
Putting the value of
\[a = 2, b = 1, c = k\]
\[D = 1 - 8k \geq 0\]
\[ \Rightarrow 8k \leq 1\]
\[ \Rightarrow k \leq \frac{1}{8}\]
Therefore, the value of \[k \leq \frac{1}{8}\].
APPEARS IN
संबंधित प्रश्न
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solve the following quadratic equations by factorization:
`sqrt2x^2-3x-2sqrt2=0`
Solve the following quadratic equations by factorization:
`7x + 3/x=35 3/5`
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
If the equation x2 − bx + 1 = 0 does not possess real roots, then
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solve equation using factorisation method:
`6/x = 1 + x`
Solve equation using factorisation method:
2x2 – 9x + 10 = 0, when:
- x ∈ N
- x ∈ Q
In each of the following, determine whether the given values are solution of the given equation or not:
2x2 - x + 9 = x2 + 4x + 3; x = 2, x = 3
Solve the following equation by factorization
x2 – (p + q)x + pq = 0
The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
In an auditorium, the number of rows are equal to the number of seats in each row.If the number of rows is doubled and number of seats in each row is reduced by 5, then the total number of seats is increased by 375. How many rows were there?
(x – 3) (x + 5) = 0 gives x equal to ______.
