Advertisements
Advertisements
Question
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
Options
0
4
0 and 4
0 or 4
Advertisements
Solution
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is 0 or 4.
Explanation:
Given quadratic equation be,
kx2 + kx + 1 = 0
On comparing with ax2 + bx + c = 0
We have, a = k; b = k; c = 1
Here D = b2 – 4ac
= k2 – 4k
Since given equation has equal roots
∴ D = 0
`\implies` k2 – 4k = 0
`\implies` k(k – 4) = 0
`\implies` k = 0 or 4
RELATED QUESTIONS
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
2x2 - (3k + 1)x - k + 7 = 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
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
(x2 + 1)2 – x2 = 0 has:
Every quadratic equation has exactly one root.
A quadratic equation with integral coefficient has integral roots. Justify your answer.
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
