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)`
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
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
Equation (x + 1)2 – x2 = 0 has ____________ real root(s).
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
If x2 (a2 + b2) + 2x (ac + bd) + c2 +d2 = 0 has no real roots, then:
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
