Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
Advertisements
उत्तर
The given quadric equation is x2 - 2kx + 7k - 12 = 0, and roots are real and equal
Then find the value of k.
Here,
a = 1, b = -2k and c = 7k - 12
As we know that D = b2 - 4ac
Putting the value of a = 1, b = -2k and c = 7k - 12
= (-2k)2 - 4 x (1) x (7k - 12)
= 4k2 - 28k + 48
The given equation will have real and equal roots, if D = 0
4k2 - 28k + 48 = 0
4(k2 - 7k + 12) = 0
k2 - 7k + 12 = 0
Now factorizing of the above equation
k2 - 7k + 12 = 0
k2 - 4k - 3k + 12 = 0
k(k - 4) - 3(k - 4) = 0
(k - 3)(k - 4) = 0
So, either
k - 3 = 0
k = 3
Or
k - 4 = 0
k = 4
Therefore, the value of k = 4, 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`
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 - 24abcdx + 16c2d2 = 0
Determine the nature of the roots of the following quadratic equation:
(b + c)x2 - (a + b + c)x + a = 0
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 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
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
`(2)/x^2 - (5)/x + 2` = 0
Solve for x: (x2 - 5x)2 - 7(x2 - 5x) + 6 = 0; x ∈ R.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 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 quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
(x2 + 1)2 – x2 = 0 has:
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 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.
