For the equation |x2 - 2 x - 3|=b , which of the following statements is true?

Question

For the equation |x2 - 2 x - 3|=b , which of the following statements is true? (A) For b < 0 , there are no solutions (B) For b=0 , there are three solutions (C) For 0 < b < 4 , there are two solutions (D) For b=4 , there are four solutions

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-j21oimwtsdymcsx5.jpg" /> b < 0 arrow no solution b=0 arrow two solutions 0 < b < 4 arrow four solutions b=4 arrow three solutions

Q. For the equation $∣ ∣ x^{2} - 2 x - 3 ∣ ∣ = b$ , which of the following statements is true?

For $b < 0$ , there are no solutions

For $b = 0$ , there are three solutions

For $0 < b < 4$ , there are two solutions

For $b = 4$ , there are four solutions

$b < 0 \to$ no solution
$b = 0 \to$ two solutions
$0 < b < 4 \to$ four solutions
$b = 4 \to$ three solutions

Q. For the equation ∣∣​x2−2x−3∣∣​=b , which of the following statements is true?

For b<0 , there are no solutions

For b=0 , there are three solutions

For 0<b<4 , there are two solutions

For b=4 , there are four solutions