Advertisements
Advertisements
प्रश्न
Every quadratic equation has at least two roots.
विकल्प
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
For example, a quadratic equation x2 – 4x + 4 = 0 has only one root which is 2.
APPEARS IN
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Solve the following quadratic equation using formula method only
`3"x"^2 + 2 sqrt 5x - 5 = 0 `
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
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`
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Find the values of k for which each of the following quadratic equation has equal roots: x2 – 2kx + 7k – 12 = 0 Also, find the roots for those values of k in each case.
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.
Every quadratic equation has exactly one root.
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 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least is ______.
