Question

If the roots of the quadratic equation
4x^2 + px +5 = 0 are a and a+2, find the real values of p .

Answer 1

Recall that for a quadratic equation that is in the form
x^2 + bx + c = 0
the sum of the roots is equal to -b, and
the product of roots is equal to c.
Therefore, we change the form of the given equation by this form,
4x^2 + px +5 = 0
x^2 + (p/4)x + 5/4 = 0
Then we set up the equations using the sum & product of roots:
a + a + 2 = -p/4
a(a+2) = 5/4
From the second equation, you can get the value of a:
a(a+2) = 5/4
(a^2 + 2a = 5/4)*4
4a^2 + 8a = 5
4a^2 + 8a - 5 = 0
(2a + 5)(2a - 1) = 0
a = -5/2, and
a = 1/2
Now substitute these values of a to the first equation. You should have two values for p.

Hope this helps~ :)