Advertisements
Advertisements
Question
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
Advertisements
Solution
Given quadratic equation is 2kx2 – 40x + 25 = 0
On comparing the above equation with ax2 + bx + c = 0, we get
a = 2k, b = –40, c = 25
For real and equal roots, D = 0
i.e., b2 – 4ac = 0
or, (–40)2 – 4(2k)(25) = 0
⇒ 1600 – 200k = 0
⇒ 200k = 1600
⇒ k = 8
APPEARS IN
RELATED QUESTIONS
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Equation (x + 1)2 – x2 = 0 has ____________ real root(s).
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
Let α and β be the roots of the equation, 5x2 + 6x – 2 = 0. If Sn = αn + βn, n = 1, 2, 3, ....., then ______.
