Question

Determine the greatest integral value of k for which 2x^2-kx+2=0 will have non-real roots (HINT:USE QUADRATIC INEQUALITIES TO DETERMINE THE SOLUTION)

Answer 1

$\textbf{Concept:}$

$\text{The condition for the roots of the equation}$}

$\text{ ax^2+bx+c=0 to be non-real is}$

$\bf\,b^2-4ac<0$

$\text{Given equation is}$

$2x^2-kx+2=0$

$\text{Here, a=2, b=-k, c=2}$

$\text{Now,}$

$b^2-4ac<0$

$\implies\,(-k)^2-4(2)(2)<0$

$\implies\,k^2-16<0$

$\implies\,k^2<16$

$\implies\bf\,-4<k<4$

$\therefore\textbf{The greatest integral value of k is 4}$

Find more:

If α and β be the roots of the equation x² + 2x + 2 = 0, then the least value of n for which (α/β)ⁿ = 1

is:

(A) 4 (B) 2

(C) 5 (D) 3

https://brainly.in/question/16069969