Advertisements
Advertisements
प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
उत्तर
The given quadric equation is 2x2 + 3x + k = 0, and roots are real.
Then find the value of k.
Here, a = 2, b = 3 and c = k
As we know that D = b2 - 4ac
Putting the value of a = 2, b = 3 and c = k
= 32 - 4 x (2) x (k)
= 9 - 8k
The given equation will have real roots, if D ≥ 0
9 - 8k ≥ 0
8k ≤ 9
k ≤ 9/8
Therefore, the value of k ≤ 9/8.
APPEARS IN
संबंधित प्रश्न
Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Every quadratic equation has at least two roots.
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
