Question

If the length of $x-$ intercept made by the graph of $f\left(x\right)=4x^2-10x+4$ is $k$, then the value of $\left[k\right]$ is
(where [.] denotes the greatest integer function)

• A. 1.0
• B. 1
• C. 1.00

Answer 1

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

Let $f\left(x\right)=4x^2-10x+4=0$ has roots as $\alpha ,\beta$
Now,
$4x^2-10x+4=0\Rightarrow 4x^2-8x-2x+4=0\Rightarrow (x-2)(4x-2)=0\Rightarrow x=\frac{1}{2},2$
$x-$ intercept made by the graph is $k$
$k=|\alpha -\beta |\Rightarrow k=2-\frac{1}{2}=\frac{3}{2}$
$\therefore \left[k\right]=1$