If the equaion `x^(2) + ax+ b = 0` has distinct real roots and `x^(2) + a|x| +b = 0` has only one real root, then

Options

A. `b = 0 , a gt 0 `
B. b = 0, a `lt` 0
C. ` b gt 0, a lt 0 `
D. `b lt 0, a gt 0 `

Answer

1

Explanation

Since the equation `x^(2) + ax + b = 0 ` has distinct real roots and
`x^(2) + a|x| + b = 0 ` has only one real root, so one root of the
equation `x^(2) + ax + b= 0` will be zero and other root will be
negative . Hence b = 0 and ` a gt 0 ` .
Graph of ` y = ax^(2) + bx + c ` according Graph of ` y = ax^(2) + b |x| + c`
to conditions given in question