Advertisements
Advertisements
प्रश्न
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Advertisements
उत्तर
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
APPEARS IN
संबंधित प्रश्न
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
If the ratio of the roots of the equation
lx2 + nx + n = 0 is p: q, Prove that
`sqrt(p/q) + sqrt(q/p) + sqrt(n/l) = 0.`
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least 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.
