Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
Advertisements
उत्तर
The given quadric equation is (k + 1)x2 + 2(k + 3)x + (k + 8) = 0, and roots are real and equal
Then find the value of k.
Here,
a = (k + 1), b = 2(k + 3) and c = (k + 8)
As we know that D = b2 - 4ac
Putting the value of a = (k + 1), b = 2(k + 3) and c = (k + 8)
= (2(k + 3))2 - 4 x (k + 1) x (k + 8)
= (4k2 + 24k + 36) - 4(k2 + 9k + 8)
= 4k2 + 24k + 36 - 4k2 - 36k - 32
= -12k + 4
The given equation will have real and equal roots, if D = 0
-12k + 4 = 0
12k = 4
k = 4/12
k = 1/3
Therefore, the value of k = 1/3.
APPEARS IN
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
Which of the following equations has two real and distinct roots?
