Find the values of $k$ for which the following equations have real roots.
$k x (x - 3) + 18 = 0$

Open in App

Solution

$k x (x - 3) + 18 = 0$
$k x^{2} - 3 k x + 18 = 0$ and $k \neq 0$
This is in the form of $a x^{2} + b x + c = 0$
Here $a = k, b = - 3 k, c = 18$
For the equation to have real roots ,
discriminant $\geq 0 ⟹ (- 3 k)^{2} - 4 (k) (18) \geq 0$
$9 k^{2}$ - $(72) (k)$ $\geq 0$
$k (k - 8) \geq 0$
$k ϵ (8, \infty)$ & $k ϵ (- \infty, 0)$

Suggest Corrections

Similar questions

Q. Find the values of

k

for which the following equations have real roots.

k x (x - 2 \sqrt{5}) + 10 = 0

Q. The value of

k

for which the roots are real and equal of the following equations

k x (x - 2) + 6 = 0

is ____

Q. Find the values of k for which the quadratic equation,

k x (x - 3) + 9 = 0

has real equal roots.

Q. Find the values of k for which the following equations have real roots

(i)

(ii)

(iii)

x^{2} - 4 k x + k = 0

(iv)

k x (x - 2 \sqrt{5}) + 10 = 0

(v)

k x (x - 3) + 9 = 0

(vi)

4 x^{2} + k x + 3 = 0

Find the values of k for which th efollowing equations have real roots.
$(i) 2 x^{2} + k x + 3 = 0 (i i) k x (x - 2) + 6 = 0 (i i i) x^{2} - 4 k x + k = 0 (i v) k x (x - 2 \sqrt{5}) + 10 = 0 (v) k x (x - 3) + 9 = 0 (v i) 4 x^{2} + k x + 3 = 0$

Join BYJU'S Learning Program

Find the values of k for which the following equations have real roots.kx(x−3)+18=0

kx(x−3)+18=0kx2−3kx+18=0 and k≠0This is in the form of ax2+bx+c=0Here a=k,b=−3k,c=18For the equation to have real roots ,discriminant ≥0⟹(−3k)2−4(k)(18)≥09k2-(72)(k)≥0k(k−8)≥0kϵ(8,∞) & kϵ(−∞,0)

Find the values of $k$ for which the following equations have real roots.
$k x (x - 3) + 18 = 0$