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CBSE Class 10 Answered

If a,b,c are real numbers such that ac not equal to 0 ,then show that at least one of the equations ax^2+bx+c=0 and -ax^2+bx+c=0 has real roots
Asked by samrajnydas | 25 Oct, 2018, 11:50: AM
answered-by-expert Expert Answer
begin mathsize 16px style Given space colon space ac space not equal to 0
In space ax squared plus bx plus straight c equals 0 comma
straight D subscript 1 space equals space straight b squared space minus space 4 ac space.... left parenthesis straight i right parenthesis
minus ax squared plus bx plus straight c equals 0
straight D subscript 2 space equals space straight b squared space plus space 4 ac space.... left parenthesis ii right parenthesis
Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
straight D subscript 1 space plus space straight D subscript 2 space equals space 2 straight b squared space greater-than or slanted equal to space 0
rightwards double arrow Atleast space one space of space straight D subscript 1 space and space straight D subscript 2 space greater-than or slanted equal to 0.
Therefore space atleast space one space ofthe space equations space ax squared plus bx plus straight c equals 0 space and space minus ax squared plus bx plus straight c equals 0 space has space real space roots. end style
Answered by Yasmeen Khan | 25 Oct, 2018, 12:18: PM
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