Question

If the equation `ax^(2) + bx + c = 0, a,b, c, in` R have non -real
roots, then
A. `c(a - b +c)gt 0`
B. `c (a + b + c) gt 0 `
C. `c( 4a - 2b + c) gt0 `
D. none of these

Answer 1

Correct Answer - 1,2,3
Since the roots if ` ax^(2) + bx + c = 0 ` are nonreal , so `f(x) = ax^(2) + bx + c `
Will have same sign for every value of x. Hence,
` f(0) = c. f(1) = a + b + c, f (-1) = a - b +c`
` f(-2) = 4 a - 2b + c `
`rArr c (a +b + c) gt 0, c(a - b + c) gt 0 , c (4a - 2b + c ) gt 0 ` .