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CBSE Class 10 Answered

With carrying out actual factorisation and using the relation between find the roots of 2x^2+9x+7
Asked by origami & craft | 25 Mar, 2019, 09:53: PM
answered-by-expert Expert Answer
2x2 +9x +7 = 0
 
By factorising:
 
2x2 +2x +7x +7 = 0
 
2x(x+1) +7(x+1) = 0
 
( 2x +7) (x+1) = 0
 
hence roots are x = -1 and x = -7/2
 
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2x2 +9x +7 = 0
 
if α and β are roots of equation ax2 +bx +c =0, sum of roots,  α+β =  -b/a  and product of roots , αβ = c/a
 
α+β = -9/2  ..........(1)
 
αβ = 7/2  ....................(2)
 
(α + β )2 - 4αβ = (α - β )2
 
(-9/2)2 - 4(7/2) = (81/4) - 14 = 25/4  = (α - β )2  or (α - β ) = 5/2 ....................(3)
 
By solving eqn.(1) and eqn.(3), we get α = -1  and β = -7/2
Answered by Thiyagarajan K | 26 Mar, 2019, 09:55: AM
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