Advertisements
Advertisements
Question
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
Advertisements
Solution
`x^2 - (1)/(2)x + 4` = 0
Here a = 1, b = `-(1)/(2)`, c = 1
∴ D = b2 - 4ac
= `(-1/2) - 4 xx 1 xx 4`
= `(1)/(4) - 16`
= `-(63)/(4)`
∵ D < 0
∴ Roots are not real.
APPEARS IN
RELATED QUESTIONS
Determine the nature of the roots of the following quadratic equation:
`3/5x^2-2/3x+1=0`
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
The quadratic equation whose one rational root is `3 + sqrt2` is
Every quadratic equation has at least one real root.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
