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
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
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 roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Every quadratic equation has at least two roots.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
