Question

If the equation $x^2-4x+m=0$ has real roots, then the maximum value of $m$ is

• A. 04
• B. 4
• C. 4.00
• D. 4.0

Answer 1

Answer: (A), (B), (C), (D)

For quadratic equation $a{x}^2+bx+c=0,a\ne 0$
Nature of roots is given by discriminant $D=b^2-4ac$ as $\left(i\right)D>0\Rightarrow \text{Real and Distinct roots}\left(ii\right)D=0\Rightarrow \text{Real and equal roots}\left(iii\right)D<0\Rightarrow \text{Non real or imaginary roots}$

Given that $x^2-4x+m=0$ has real roots
$\Rightarrow D=(-4{)}^2-4(1\left)\right(m)\ge 0$
$\Rightarrow 16-4m\ge 0$
$\Rightarrow 4m\le 16\Rightarrow m\le 4$
$\therefore$ Maximum value of $m=4$