Question

if α and β are zeros of the polynomial x²+7x+10 then find the value of 1/∞²+1/β²​

Answer 1

Answer:

29/100

Step-by-step explanation:

Given,

α and β are zeros of the polynomial x²+7x+10 .

To Find :-

Value of :-

1/α² + 1/β²

How To Do :-

We need to find the value of the zeroes of the polynomial by using the quadratic formula. After obtaining the value of the zeroes of the polynomial we need to substitute in them , then we will get the required value.

Formula Required :-

Considering general form of quadratic polynomial as 'ax² + bx + c' ,

Quadratic formula :-

$\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Solution :-

Comparing 'ax² + bx + c' with 'x²+7x+10' :-

→ a = 1 , b = 7 , c = 10

Substituting in the quadratic formula :-

$=\dfrac{-7\pm\sqrt{(7)^2-4(1)(10)}}{2(1)}$

$=\dfrac{-7\pm\sqrt{49-40}}{2}$

$=\dfrac{-7\pm\sqrt{9}}{2}$

$=\dfrac{-7\pm 3}{2}$

x =( - 7 + 3)/2 , (- 7 - 3)/2

x = - 4/2 , - 10 /2

x = - 2 , - 5

∴ α = - 2 , β = - 5

Taking L.C.M as '100' :-

= (25 + 4)/100

= 29/100

∴ 1/α² + 1/β² = 29/100