Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
Advertisements
उत्तर
The given quadric equation is 4x2 + kx + 9 = 0, and roots are real and equal
Then find the value of k.
Here, a = 4, b = k and c = 9
As we know that D = b2 - 4ac
Putting the value of a = 4, b = k and c = 9
= (k)2 - 4 x (4) x (9)
= k2 - 144
The given equation will have real and equal roots, if D = 0
Thus,
k2 - 144 = 0
k2 = 144
`k=sqrt144`
k = ± 12
Therefore, the value of k = ± 12.
APPEARS IN
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 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
4x2 + 12x + 9 = 0
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
Find the discriminant of the following equations and hence find the nature of roots: 2x2 + 15x + 30 = 0
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x2 – 3x + 4 = 0
A quadratic equation with integral coefficient has integral roots. Justify your answer.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x(1 – x) – 2 = 0
If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.
