Advertisements
Advertisements
प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
उत्तर
The given quadric equation is 2x2 + kx - 4 = 0, and roots are real.
Then find the value of k.
Here, a = 2, b = k and c = -4
As we know that D = b2 - 4ac
Putting the value of a = 2, b = k and c = -4
= k2 - 4 x (2) x (-4)
= k2 + 32
The given equation will have real roots, if D ≥ 0
k2 + 32
Since left hand side always positive.
So k ∈ R
APPEARS IN
संबंधित प्रश्न
Find that value of p for which the quadratic equation (p + 1)x2 − 6(p + 1)x + 3(p + 9) = 0, p ≠ − 1 has equal roots. Hence find the roots of the equation.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
