Consider the two sets: $A = \{m \in \mathbb{R} : ext{both the roots of } x^{2} - (m+1)x + m + 4 = 0 ext{ are real}\}$ and $B = [-3, 5)$ Which of the following is not true?

Question

Consider the two sets: $A = \{m \in \mathbb{R} : 	ext{both the roots of } x^{2} - (m+1)x + m + 4 = 0 	ext{ are real}\}$ and $B = [-3, 5)$ Which of the following is not true?

Aicharya · Accepted Answer

Since both roots are real m + 1 2 - 4 m + 4 &#8805; 0 &#8658; m 2 - 2 m - 15 &#8805; 0 &#8658; m - 5 m + 3 &#8805; 0 &#8658; m &#8712; ( - &#8734; , - 3 ] &#8746; [ 5 , &#8734; ) &#8658; A = ( - &#8734; , - 3 ] &#8746; [ 5 , &#8734; ) A - B = - &#8734; , - 3 &#8746; [ 5 , &#8734; ) A &#8745; B = - 3 B - A = - 3 , 5 A &#8746; B = R

Consider the two sets: $A = \{m \in \mathbb{R} : \text{both the roots of } x^{2} - (m+1)x + m + 4 = 0 \text{…

Solution