Advertisements
Advertisements
Question
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
Advertisements
Solution
6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
If x = `(-1)/(2)`, then
= `6(-1/2)^2 - (-1/2) - 2`
= `6 xx (1)/(4) + (1)/(2) - 2`
= `(3)/(2) + (1)/(2) - 2`
= `(4)/(2) - 2` = 0
∴ x = `(-1)/(2)` is its root
If x = `(2)/(3)`, then
= `6 xx (4)/(9) - (2)/(3) - 2`
= `(8)/(3) - (2)/(3) - 2`
= `(6)/(3) - 2` = 0
∴ x = `(2)/(3)` is also its root.
Hence `(-1)/(2), (2)/(3)` are both its root.
APPEARS IN
RELATED QUESTIONS
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 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 ______.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
