Advertisements
Advertisements
प्रश्न
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
`10x -(1)/x` = 3
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
If the ratio of the roots of the equation
lx2 + nx + n = 0 is p: q, Prove that
`sqrt(p/q) + sqrt(q/p) + sqrt(n/l) = 0.`
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
Every quadratic equation has at least one real root.
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
