Advertisements
Advertisements
प्रश्न
Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
Advertisements
उत्तर
The given quadric equation is 2x2 + kx − 8 = 0 , and roots are real.
Then find the value of k.
Here, a = 2 , b = k and, c = -8
As we know that `D =b^2 - 4ac`
Putting the value of a = 2 , b = k and, c = -8
` = (k)^2 - 4 xx 2 xx (-8)`
= `k^2 + 64`
The given equation will have real roots, if D > 0
I.e., k2 + 64 > 0 which is true for all real values of k
Therefore, for all real values of k, the given equation has real roots.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
Solve each of the following equations by factorization :
`6/x=1+x`
The sum of natural number and its positive square root is 132. Find the number.
Find two consecutive multiples of 3 whose product is 648.
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
Solve the following quadratic equation by factorisation.
7m2 = 21m
The values of k for which the quadratic equation \[16 x^2 + 4kx + 9 = 0\] has real and equal roots are
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
If car A use 4 litre of petrol more than car B in covering the 400 km, write down and equation in x and solve it to determine the number of litre of petrol used by car B for the journey.
Solve the following equation by factorization
a2x2 + (a2+ b2)x + b2 = 0, a ≠ 0
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 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.
Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
If x4 – 5x2 + 4 = 0; the values of x are ______.
