Advertisements
Advertisements
प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
Advertisements
उत्तर
The given quadric equation is 2x2 − 5x − k = 0, and roots are real
Then find the value of k.
Here,
a = 2
b = −5
c = k
As we know that D = b2 − 4ac
Putting the value of a = 2, b = −5 and c = k
= (−5)2 − 4 × (2) × (−k)
= 25 + 8k
The given equation will have real roots, if D ≥ 0
25 + 8k ≥ 0
8k ≥ −25
k ≥ `−25/8`
Therefore, the value of k ≥ `−25/8`
संबंधित प्रश्न
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Form the quadratic equation if its roots are –3 and 4.
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
Solve x2/3 + x1/3 - 2 = 0.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
In each of the following determine the; value of k for which the given value is a solution of the equation:
x2 + 2ax - k = 0; x = - a.
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’.
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
Solve the equation: 3x2 – 8x – 1 = 0 for x.
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
