Question

value of k for which quadratic equation 3x2-kx=5=0 has two equal root is​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

k = $2\sqrt{15}$

Step-by-step explanation:

Given equation -

$3x^{2}-kx-5=0$            ----------------------- 1

Let A and B are two roots of given equation.

Since equation has two equal roots. Then

A = B

Compare equation 1 with the general quadratic equation

$ax^{2}+bx+c=0$

Here a =3, b = -k  and c = -5

For any quadratic equation-

Sum of roots = $-\dfrac{b}{a}$

A + B = $-\dfrac{b}{a}$

         = $-\dfrac{-k}{3}$

A + B = $\dfrac{k}{3}$  

A + A = $\dfrac{k}{3}$  

2A = $\dfrac{k}{3}$  

A = $\dfrac{k}{6}$          

Product of roots = $\dfrac{c}{a}$

AB = $\dfrac{c}{a}$

A.A = $\dfrac{-5}{3}$

A^{2} = $\dfrac{-5}{3}$    --------------------- 2

Put A =  $\dfrac{k}{6}$ in equation 2, we get -

$\dfrac{k}{6} = \dfrac{-5}{3}$

$\dfrac{k^{2} }{36}$ = $\dfrac{-5}{3}$

$k^{2} = \dfrac{-5 * 36}{3}$

$k^{2} = -5 × 12</p><p>[tex]k^{2} = -60</p><p>[tex]k^{2} = 60i^{2}$

k = $\sqrt{60i^{2} }$

k = $2\sqrt{15} i$

k = $2\sqrt{15}$