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`
APPEARS IN
संबंधित प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Determine the nature of the roots of the following quadratic equation :
x2 -4x + 4=0
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
48x² – 13x -1 = 0
`10x -(1)/x` = 3
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
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Choose the correct answer from the given four options :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
If one root of the quadratic equation 2x2 + kx – 6 = 0 is 2, the value of k is:
If –5 is a root of the quadratic equation 2x2 + px – 15 = 0, then:
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
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.
Equation 2x2 – 3x + 1 = 0 has ______.
