Question

If alpha and beta are the zeros of the equation 2x^2+7x+5 =0 then write a quadratic equation whose roots are 2a+3 and 2b+3

Answer 1

a and b are the roots of 2x^2 + 7x + 5 = 0.

Therefore, a + b = -7/2 and ab = 5/2.

Now for our new quadratic,

Sum of roots = 2a + 3 + 2b + 3 = 2(a + b) + 6 = 2(-7/2) + 6 = -7 + 6 = -1.

Product of roots = (2a + 3)(2b + 3) = 4ab + 6a + 6b + 9

                                                        = 4ab + 6(a + b) + 9

                                                        = 4(5/2) + 6(-7/2) + 9

                                                        = 10 - 21 + 9

                                                        = -2.

So the new quadratic equation is x^2 + x - 2 = 0.