Question

The solutions to the equation x^2 px q are x = 5 root , find values of p and q

Answer 1

The values of p and q for the quadratic equation with a root of √5 are p = 2√5 and q = 5.

Step-by-step explanation:

We need to find the values of p and q for the quadratic equation x² + px + q = 0, given that one of the solutions is x = √5. Since √5 is a root, squaring it should yield 5, the same value as x. This implies that the other root of the equation should also be √5 due to the nature of quadratic equations having two roots. Therefore, by the sum and product of roots for quadratic equations, we have:

- Sum of the roots (p) = √5 + √5 = 2√5

- Product of the roots (q) = (√5) (√5) = 5

So, the values are p = 2√5 and q = 5.