Advertisements
Advertisements
Question
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
Advertisements
Solution
6x2 - x - 2 = 0; x = `(2)/(3), -1`
Now put x = -1 in L.H.S. of equation.
L.H.S. = 6 x (-1)2 - (-1) -2
= 6 + 1 - 2
= 7 - 2 = 5 ≠ 0 ≠ R.H.S.
Hence, x = -1 is not a root of the equation.
Put x = `(2)/(3)` in L.H.S. of equation.
L.H.S. = 6 x `(2/3)^2 - (2)/(3) -2`
= `(24)/(9) - (2)/(3) - 2`
= `(8)/(3) - (2)/(3) - 2 = 0`
= 8 - 8 = 0
= R.H.S.
Hence, x = `(2)/(3)` is a solution of given equation.
RELATED QUESTIONS
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 - 24abcdx + 16c2d2 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
Find the values of k for which the roots are real and equal in each of the following equation:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
ax2 + (4a2 - 3b)x - 12 ab = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
Which of the following equations has imaginary roots?
