1. Find the roots of Quadratic Equation `x^2+10x-56=0` by the method of perfect square
Solution:
`x^2+10x-56=0`
`=>x^2+10x-56 = 0`
Comparing the given equation with the standard quadratic equation `ax^2+bx+c=0,`
we get, `a=1, b=10, c=-56.`
`:. Delta=b^2-4ac`
`=(10)^2-4 (1) (-56)`
`=100+224`
`=324`
`:. sqrt(Delta)=sqrt(324)=18`
Now, `alpha=(-b+sqrt(Delta))/(2a)`
`=(-(10)+18)/(2*1)`
`=8/2`
`=4`
and, `beta=(-b-sqrt(Delta))/(2a)`
`=(-(10)-18)/(2*1)`
`=-28/2`
`=-14`
2. Find the roots of Quadratic Equation `25x^2-30x+9=0` by the method of perfect square
Solution:
`25x^2-30x+9=0`
`=>25x^2-30x+9 = 0`
Comparing the given equation with the standard quadratic equation `ax^2+bx+c=0,`
we get, `a=25, b=-30, c=9.`
`:. Delta=b^2-4ac`
`=(-30)^2-4 (25) (9)`
`=900-900`
`=0`
`:. sqrt(Delta)=sqrt(0)=0`
Now, `alpha=(-b+sqrt(Delta))/(2a)`
`=(-(-30)+0)/(2*25)`
`=30/50`
`=3/5`
and, `beta=(-b-sqrt(Delta))/(2a)`
`=(-(-30)-0)/(2*25)`
`=30/50`
`=3/5`
This material is intended as a summary. Use your textbook for detail explanation.
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