Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Form the quadratic equation if its roots are –3 and 4.
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 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
`"x"^2 + 1/2 "x" = 3`
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
In each of the following determine the; value of k for which the given value is a solution of the equation:
x2 + 2ax - k = 0; x = - a.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 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.
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4 , b = ______ , c = 3
b2 – 4ac = (– 5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
(x2 + 1)2 – x2 = 0 has ______.
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
Solve for x: 9x2 – 6px + (p2 – q2) = 0
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
