Advertisements
Advertisements
Question
Every quadratic equation has at least two roots.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
For example, a quadratic equation x2 – 4x + 4 = 0 has only one root which is 2.
APPEARS IN
RELATED QUESTIONS
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 - 24abcdx + 16c2d2 = 0
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:
2x2 + 3x + k = 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 :
16x2 = 24x + 1
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
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:
kx2 + 2x + 3k = 0
Choose the correct answer from the given four options :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
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) + 2 = 0
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
The roots of quadratic equation x2 – 1 = 0 are ______.
One root of equation 3x2 – mx + 4 = 0 is 1, the value of m is ______.
