Question

If alpha and beta are the roots of the equation x^2-px+q=0 from the equation whose roots are(alpha×beta + alpha + beta) and (alpha × beta - alpha- beta) find the amplitude and modulus​

Answer 1

Answer:

Step-by-step explanation:

given :

If alpha and beta are the roots of the equation x^2-px+q=0 from the equation whose roots are(alpha×beta + alpha + beta) and (alpha × beta - alpha- beta) find the amplitude and modulus

to find :

find the amplitude and modulus

solution :

• Given that a, ß are the roots of x² + px +

• q=0

• We have a +B= -P and aß =

• Now let us consider x² + ax + b = 0 be the

• equation whose roots are (a – ß)2², (a + b)²

• Sum of roots is

• 2(a² + ß²) = 2(p² – 2q)

• ⇒a= 2(2q - p²)

• Product of roots is b = (a + b)²(a - ß)² = (p²)(p² - 4q)

• So the required equation is x² + 2(2q - p²)x+p² (p²4q) = 0

• -a=

• (a − p)² + (a +ß)²