Advertisements
Advertisements
Question
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Advertisements
Solution
The given equation is x2+k(2x+k−1)+2=0.
⇒x2+2kx+k(k−1)+2=0
So, a = 1, b = 2k, c = k(k − 1) + 2
We know D=b2−4ac
⇒D=(2k)2 − 4 × 1 × [k(k − 1) + 2]
⇒D=4k2 − 4[k2 − k + 2]
⇒D=4k2 − 4k2 + 4k − 8
⇒D=4k − 8 = 4(k − 2)
For equal roots, D = 0
Thus, 4(k − 2) = 0
So, k = 2.
APPEARS IN
RELATED QUESTIONS
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Without solving, examine the nature of roots of the equation 2x2 + 2x + 3 = 0
If the roots of the equation (b − c) x2 + (c − a) x + (a − b) = 0 are equal, then prove that 2b = a + c.
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
48x² – 13x -1 = 0
Choose the correct answer from the given four options :
Which of the following equations has two distinct real roots?
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
