Advertisements
Advertisements
प्रश्न
Every quadratic equation has at least one real root.
पर्याय
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
For example, equation x2 + 4 = 0 has no real root.
APPEARS IN
संबंधित प्रश्न
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.
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
If the roots of the equation (b − c) x2 + (c − a) x + (a − b) = 0 are equal, then prove that 2b = a + c.
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
`(2)/x^2 - (5)/x + 2` = 0
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x2 – 3x + 4 = 0
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
