Question

If a and b are the zeroes of P(X)=x2+7x+7 Find a/b + b/a +2

Answer 1

Answer:

a/b+b/a+2=7

Step-by-step explanation:

Given polynomial,

$p(x) = {x}^{2} + 7x + 7$

we know that,

sum of zeros= -(coefficient of x)/coefficient of x^2.

and,product of zeros= constant term/coefficient of x^2.

therefore,

$(a + b) = \frac{ - 7}{1} = - 7. \\ (ab) = \frac{7}{1} = 7$

now,

$\frac{a}{b} + \frac{b}{a } + 2 = \frac{ {a}^{2} + {b}^{2} + 2ab}{ab} \\ = \frac{ {(a + b)}^{2} }{ab} = \frac{ {( - 7)}^{2} }{7} \\ = \frac{49}{7} = 7$

hope this helps