Question

If a, ß are the zeroes of the quadratic polynomial p(x) = 2x² +11x+5. Find the value of 1/a + 1/B - 2aB​

Answer 1

Step-by-step explanation:

Given :-

a, ß are the zeroes of the quadratic polynomial p(x) = 2x^2 +11x+5.

To find:-

Find the value of 1/a + 1/ß-2aß?

Solution:-

Given Quadratic Polynomial P(x)=2x^2 +11x+5.

On Comparing this with the standard quadratic Polynomial ax^2+bx+c

We have,

a =2

b=11

c=5

if a, ß are the zeroes of P(x) then

Sum of the zeroes = a+ß = -b/a

=> a+ß = -11/2 --------------(1)

Product of the zeroes = aß = c/a

=> aß = 5/2 ----------------(2)

Now we have to find the value of

=> 1/a + 1/ß-2aß

=>(1/a + 1/ß)-2aß

=>[ (a+ß)/(aß) ]-2aß

From (1)&(2)

=>[ (-11/2)/(5/2)] - 2(5/2)

=>[ (-11/2)×(2/5)]-(10/2)

=>(-11×2)/(2×5)-(10/2)

=>(-22/10)-(10/2)

=>(-11/5)-(5)

=>[-11-(5×5)]/5

=>(-11-25)/5

=>-36/5

Therefore, 1/a + 1/ß-2aß = -36/5

Answer:-

The value of 1/a + 1/ß-2aß for the given problem is

-36/5

Used formulae:-

• The standard quadratic Polynomial ax^2+bx+c
• Sum of the zeroes = a+ß = -b/a
• Product of the zeroes = aß = c/a