Question

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

Answer 1

sum of the roots of the given equation =a+b=(-7/2)........................................(i)
product of the roots of the given equation =ab=(5/2)...........................................(ii)
sum of roots of the required equation =2a+3+2b+3= 2(a+b)+6= (-7/2)*2+6 [From (i)]
= - 1 ........(iii)
product of roots of the required equation =(2a+3)(2b+3)=4ab+6(a+b)+9
=4*(5/2)+6{-7/2)+9
=10 - 21+9 = - 2.......(iv)
we know that, we can write any Quadratic equation as,
x^2 - (sum of roots) x + (product of roots) =0
Therefore the required equation is,
x^2 + x - 2=0