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
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
If x = −2 is a root of the equation 3x2 + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x2 + k(4x + k − 1) + p = 0 are equal.
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x2 + 2(k – 4) x + 4 = 0
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Solve the equation: 3x2 – 8x – 1 = 0 for x.
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
Which of the following equations has two real and distinct roots?
