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(3k + 1)x + 8k + 1 = 0
Advertisements
उत्तर
The given quadric equation is (k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0, and roots are real and equal
Then find the value of k.
Here,
a = k + 1, b = -2(3k + 1)x and c = 8k + 1
As we know that D = b2 - 4ac
Putting the value of a = k + 1, b = -2(3k + 1)x and c = 8k + 1
= (-2(3k + 1))2 - 4 x (k + 1) x (8k + 1)
= 4(9k2 + 6k + 1) - 4(8k2 + 9k + 1)
= 36k2 + 24k + 4 - 32k2 - 36k - 4
= 4k2 - 12k
The given equation will have real and equal roots, if D = 0
4k2 - 12k = 0
k2 - 3k = 0
Now factorizing of the above equation
k(k - 3) = 0
So, either
k = 0
Or
k - 3 = 0
k = 3
Therefore, the value of k = 0, 3.
APPEARS IN
संबंधित प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Determine the nature of the roots of the following quadratic equation:
(b + c)x2 - (a + b + c)x + a = 0
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
The quadratic equation whose one rational root is `3 + sqrt2` is
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x(1 – x) – 2 = 0
Every quadratic equation has at least two roots.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
Which of the following equations has imaginary roots?
