Question

If the discriminant of the equation $3x^2-4x+k=0$ is $64$, then $k=$ _________.

• A. $-4$
• B. $4$
• C. $-8$
• D. $8$

Answer 1

Answer: (A)

$-4$

$\Rightarrow$ The given quadratic equation is $3x^2-4x+k=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $x=3,b=-4,c=k$

$\Rightarrow$ $b^2-4ac=64$ [ Given ]

$\Rightarrow$ $(-4{)}^2-4(3\left)\right(k)=64$

$\Rightarrow$ $16-12k=64$

$\Rightarrow$ $-12k=48$

$\Rightarrow$ $k=\frac{-48}{12}$

$\therefore$ $k=-4$