Advertisements
Advertisements
Question
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Advertisements
Solution
(3m + 1)x2 + 2(m + 1)x + m = 0
Here a = 3m + 1, b = 2(m + 1), c = m
D = b2 - 4ac
= [2(m + 1)]2 - 4 x (3m + 1)(m)
= 4(m2 + 2m + 1) - 12m2 - 4m
= 4m2 + 8m + 4 - 12m2 - 4m
= -8m2 + 4m + 4
∴ Roots are equal.
∴ D = 0
⇒ -8m2 + 4m + 4 = 0
⇒ 2m2 - m - 1 = 0 ...(Dividing by 4)
⇒ 2m2 - 2m + m - 1 = 0
⇒ 2m(m - 1) + 1(m - 1) = 0
⇒ (m - 1)(2m + 1) = 0
Either m - 1 = 0,
then m = 1
or
2m + 1 = 0,
then 2m = -1
⇒ m = `-(1)/(2)`.
APPEARS IN
RELATED QUESTIONS
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 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 roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
