if a and b are roots of the equation 2x^2+7x+5=0 then write a quadratic equation whose roots are 2a+3 and 2b+3
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2x²+7x+5=0
2x²+5x+2x+5=0
x(2x+5)+1(2x+5)=0
(x+1)(2x+5)=0
x=-1 and x=-5/2
therefore,a=-1 and b=-5/2
2a+3=2*-1+3
=-2+3
=1
2b+3=-5+3
=-2
sum of zeros=1-2
=-1
product of zeros=-2
using formula
x²+x-2 is the required equation
2x²+5x+2x+5=0
x(2x+5)+1(2x+5)=0
(x+1)(2x+5)=0
x=-1 and x=-5/2
therefore,a=-1 and b=-5/2
2a+3=2*-1+3
=-2+3
=1
2b+3=-5+3
=-2
sum of zeros=1-2
=-1
product of zeros=-2
using formula
x²+x-2 is the required equation
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