Let p, q [ ] R.

Question

Let p, q $$ \in $$ R. If 2 - $$\sqrt 3$$ is a root of the quadratic
equation, x2 + px + q = 0, then :

Accepted Answer

If a quadratic equation with rational coefficient has one irrational root then other root will be the conjugate of the irrational root.

Here x2 + px + q = 0 has one root 2 - $$\sqrt 3$$.

$$ \therefore $$ Other root will be 2 + $$\sqrt 3$$.

Sum of the roots = -p = 4

and product of the roots = q = 1

You can see p2 -- 4q -- 12 = 0 satisfy value of p = -4 and q = 1.

Solutions · 1