If the equation x2+a x+b=0 has distinct real roots and x2+a|x|+b=0 has only one real root, then which of the following is true ?

Question

If the equation x2+a x+b=0 has distinct real roots and x2+a|x|+b=0 has only one real root, then which of the following is true ? (A) b=0, a>0 (B) b=0, a<0 (C) b >0, a <0 (D) b<0, a>0

Tardigrade Admin · Accepted Answer

Since the equation x2+a x+b=0 has distinct real roots and x2+a|x|+b=0 has only real root, so one root of the equation x2+a x+b=0 will be zero and other will be negative. Hence, b=0 and a>0.

Q. If the equation $x^{2} + a x + b = 0$ has distinct real roots and $x^{2} + a ∣ x ∣ + b = 0$ has only one real root, then which of the following is true ?

$b = 0, a > 0$

$b = 0, a < 0$

$b > 0, a < 0$

$b < 0, a > 0$

Since the equation $x^{2} + a x + b = 0$ has distinct real roots and $x^{2} + a ∣ x ∣ + b = 0$ has only real root, so one root of the equation $x^{2} + a x + b = 0$ will be zero and other will be negative. Hence, $b = 0$ and $a > 0$ .

Q. If the equation x2+ax+b=0 has distinct real roots and x2+a∣x∣+b=0 has only one real root, then which of the following is true ?

b=0,a>0

b=0,a<0

b>0,a<0

b<0,a>0