Menu Close

3x-2-7-x-m-5-0-At-what-value-of-m-can-the-equation-have-three-roots-

Tinku Tara 0 Comments
Pin




Question Number 147978 by mathdanisur last updated on 24/Jul/21
3x^2 - 7 ∣x∣ + m - 5 = 0 At what value of m can the equation have three roots
3x2−7∣x∣+m−5=0Atwhatvalueofmcantheequationhavethreeroots
Answered by Olaf_Thorendsen last updated on 24/Jul/21
In R, the equation can have two opposite solutions for x<0 (∣x∣ = −x) and two opposite solutions for x>0 (∣x∣ = x). To obtain exactly three roots, one root needs to be 0 (to be equal to its opposite). That occurs when (c/a) = ((m−5)/3) = 0 ⇒ m = 5. In this case 3x^2 = 7∣x∣ ⇒ x = 0, x = ±(7/3)
InR,theequationcanhavetwooppositesolutionsforx<0(∣x∣=−x)andtwooppositesolutionsforx>0(∣x∣=x).Toobtainexactlythreeroots,onerootneedstobe0(tobeequaltoitsopposite).Thatoccurswhenca=m−53=0⇒m=5.Inthiscase3x2=7∣x∣⇒x=0,x=±73
Commented by mathdanisur last updated on 25/Jul/21
Thankyou Ser
ThankyouSer
Answered by Rasheed.Sindhi last updated on 25/Jul/21
3x^2 - 7 ∣x∣ + m - 5 = 0 ⇒ { ((i:3x^2 - 7x =− m + 5)),((ii:3x^2 + 7x= − m + 5)) :}⇒3x^2 ^(×) −7x=3x^2 ^(×) +7x ⇒x=0 (common root of i & ii) ∵ i & ii have one root common ∴ They have total three roots ∴ The original equation has 3 roots 3x^2 - 7 ∣x∣ + m - 5 = 0 ⇒3(0)^2 −7∣0∣+m−5=0 ⇒m−5=0⇒m=5
3x2−7∣x∣+m−5=0⇒{i:3x2−7x=−m+5ii:3x2+7x=−m+5⇒3x2×−7x=3x2×+7x⇒x=0(commonrootofi&ii)∵i&iihaveonerootcommon∴Theyhavetotalthreeroots∴Theoriginalequationhas3roots3x2−7∣x∣+m−5=0⇒3(0)2−7∣0∣+m−5=0⇒m−5=0⇒m=5
Commented by mathdanisur last updated on 25/Jul/21
Thank you Ser
ThankyouSer

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *