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
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
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(x - 2) + 6 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b2 = ac.
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
`(2)/x^2 - (5)/x + 2` = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 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)
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4 , b = ______ , c = 3
b2 – 4ac = (– 5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
The roots of the equation 7x2 + x – 1 = 0 are:
A quadratic equation with integral coefficient has integral roots. Justify your answer.
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
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 ______.
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 ______.
Which of the following equations has two real and distinct roots?
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
