Advertisements
Advertisements
Question
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Advertisements
Solution
x2 – x + 1 = 0; 1, – 1
Where x = 1, then
(1)2 – 1 + 1 = 1 – 1 + 1 = 1 ≠ 0
∴ x = 1 does not satisfy it
and (-1)2 - (-1) + 1 = 0
1 + 1 + 1 ⇒ 3 ≠ 0
∴ x = -1, does not satisfy it
∴ x = 1, -1 are not roots of the equation.
APPEARS IN
RELATED QUESTIONS
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
48x² – 13x -1 = 0
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
The roots of the quadratic equation `2"x"^2 - 2sqrt2"x" + 1 = 0` are:
The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
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 ______.
Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.
