Advertisements
Advertisements
Question
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Advertisements
Solution
Given quadratic equation is (m + 4)x2 + (m + 1)x + 1 = 0
The quadratic equation has real and equal roots if its discriminant is zero.
`=>` D = b2 – 4ac = 0
`=>` (m + 1)2 – 4(m + 4)(1) = 0
`=>` m2 + 2m + 1 – 4m – 16 = 0
`=>` m2 – 2m – 15 = 0
`=>` m2 – 5m + 3m – 15 = 0
`=>` m(m – 5) + 3(m – 5) = 0
`=>` (m – 5)(m + 3) = 0
`=>` m = 5 or m = –3
RELATED QUESTIONS
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
Find whether the following equation have real roots. If real roots exist, find them.
`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
Solve for x: 9x2 – 6px + (p2 – q2) = 0
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
