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
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
Solve the following quadratic equations by factorization:
`7x + 3/x=35 3/5`
If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
Solve each of the following equations by factorization:
`9/2x=5+x^2`
The sum of a natural number and its square is 156. Find the number.
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples ?
Solve the following equation: a2x2 - 3abx + 2b2 = 0
Solve the following equation : x2 + 2ab = (2a + b)x
Solve the following equation: `x^2 + (a + 1/a)x + 1 = 0`
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
Solve equation using factorisation method:
2(x2 – 6) = 3(x – 4)
Solve the following quadratic equation by factorisation:
x2 + 3x - 18 = 0
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?
A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
