Advertisements
Advertisements
Question
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solution
2x2 + 5x - 6 = 0
b2 - 4ac
= (5)2 - 4(2)(-6)
= 25 + 48
= 73
Since discriminant is positive, hence the roots are real and irrational.
APPEARS IN
RELATED QUESTIONS
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
Which of the following equations has imaginary roots?
