Advertisements
Advertisements
प्रश्न
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
विकल्प
0 only
4
8 only
0, 8
Advertisements
उत्तर
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is 0, 8.
Explanation:
Given equation is 2x2 – kx + k = 0
On comparing with ax2 + bx + c = 0, we get
a = 2, b = –k and c = k
For equal roots, the discriminant must be zero
i.e., D = b2 – 4ac = 0
⇒ (–k)2 – 4(2)k = 0
⇒ k2 – 8k = 0
⇒ k(k – 8) = 0
∴ k = 0, 8
Hence, the required values of k are 0 and 8.
संबंधित प्रश्न
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
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:
`3x^2-2sqrt6x+2=0`
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(5 + 2k)x + 3(7 + 10k) = 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
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 ?
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 :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Solve the following quadratic equation using formula method only
15x2 - 28 = x
48x² – 13x -1 = 0
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
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.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
Equation 2x2 – 3x + 1 = 0 has ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
