Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
(3k+1)x2 + 2(k + 1)x + k = 0
Advertisements
उत्तर
The given quadric equation is (3k+1)x2 + 2(k + 1)x + k = 0, and roots are real and equal
Then find the value of k.
Here, a = (3k + 1), b = 2(k + 1) and c = k
As we know that D = b2 - 4ac
Putting the value of a = (3k + 1), b = 2(k + 1) and c = k
= (2(k + 1))2 - 4 x (3k + 1) x (k)
= 4(k2 + 2k + 1) - 4k(3k + 1)
= 4k2 + 8k + 4 - 12k2 - 4k
= -8k2 + 4k + 4
The given equation will have real and equal roots, if D = 0
Thus,
-8k2 + 4k + 4 = 0
-4(2k2 - k - 1) = 0
2k2 - k - 1 = 0
Now factorizing of the above equation
2k2 - k - 1 = 0
2k2 - 2k + k - 1 = 0
2k(k - 1) + 1(k - 1) = 0
(k - 1)(2k + 1) = 0
So, either
k - 1 = 0
k = 1
Or
2k + 1 = 0
2k = -1
k = -1/2
Therefore, the value of k = 1, -1/2
APPEARS IN
संबंधित प्रश्न
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
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
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
ax2 + (4a2 - 3b)x - 12 ab = 0
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 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
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to ______.
Equation 2x2 – 3x + 1 = 0 has ______.
One root of equation 3x2 – mx + 4 = 0 is 1, the value of m is ______.
