Question

If 2 is a root of the quadratic equation $3x^2$ + px - 8 = 0 and the quadratic equation 4$x^2$ - 2px + k = 0 has equal roots, The value of k is------.

Answer 1

$\Rightarrow$ $3x^2+px-8=0$

Substitute $x=2$, since $2$ is root of equation

$\Rightarrow$ $3(2{)}^2+p(2)-8=0$

$\Rightarrow$ $12+2p-8=0$

$\Rightarrow$ $4+2p=0$

$\therefore$ $p=-2$

$\Rightarrow$ $4x^2-2px+k=0$

$\Rightarrow$ $4x^2-2(-2)x+k=0$ [ Since, $p=-2$ ]

$\Rightarrow$ $4x^2+4x+k=0$

$\Rightarrow$ Here, $a=4,b=4,c=k$

$\Rightarrow$ It is given that roots are equal.

$\therefore$ $b^2-4ac=0$

$\Rightarrow$ $(4{)}^2-4(4\left)\right(k)=0$

$\Rightarrow$ $16-16k=0$

$\Rightarrow$ $16k=16$

$\therefore$ $k=1$