Let p , q ∈ Q . If 2 - 3 is a root of the quadratic equation x 2 + p x + q = 0 , then

Step-by-step solution

In given equation x 2 + p x + q = 0 ,   p ,   q ∈ Q . And, we know that the irrational roots of a quadratic equation exist in conjugate pair, if the coefficients are rational. Thus, if one root of the equation x 2 + p x + q = 0 is 2 - 3 , then, the other root will be 2 + 3 . We know that the sum and product of the roots of a quadratic equation a x 2 + b x + c = 0 are respectively - b a and c a . Therefore, the sum of roots 2 + 3 + 2 - 3 = - p ⇒ p = - 4 And, the product of roots 2 + 3 2 - 3 = q