Suppose m∈R. The quadratic equation x2−(m−3)x+m=0 has

(1) will have real and distinct roots⇔ D=(m−3)2−4m>0⇔ m2−10m+9>0⇔ m∈(−∞,1)∪(9,∞)Roots of (1) will be both positive ifD≥0,m−3>0,m>0⇒ m≥9,m>3.∴ m∈[9,∞)Roots of (1) will be negative ifD≥0,m−3 0⇒ m≤1,0<m<3Thus, m∈(0,1]For m < 0, equation has one positive and one negative root.

Suppose m∈R. The quadratic equation x2−(m−3)x+m=0 has

(1) will have real and distinct roots⇔ D=(m−3)2−4m>0⇔ m2−10m+9>0⇔ m∈(−∞,1)∪(9,∞)Roots of (1) will be both positive ifD≥0,m−3>0,m>0⇒ m≥9,m>3.∴ m∈[9,∞)Roots of (1) will be negative ifD≥0,m−3 0⇒ m≤1,0<m<3Thus, m∈(0,1]For m < 0, equation has one positive and one negative root.

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Suppose $m \in R$ . The quadratic equation $x^{2} - (m - 3) x + m = 0$ has

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

real distinct roots if and only if

$m \in (- \infty, 1) \cup (9, \infty)$

both positive roots if and only if $m \in [9, \infty)$

both negative roots if and only if $m \in (0, 1]$

at least one positive root if and only if $m \in (9, \infty)$

answer is A, B, C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

(1) will have real and distinct roots

$\begin{array}{ll} \Leftrightarrow D = (m - 3)^{2} - 4 m > 0 \\ \Leftrightarrow m^{2} - 10 m + 9 > 0 \\ \Leftrightarrow m \in (- \infty, 1) \cup (9, \infty) \end{array}$