Advertisements
Advertisements
प्रश्न
Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
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
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
Solve the following equation by factorization
4x2 = 3x
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?
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
