Question

If alpha and beta are the zeros of the polynomial p(x) = 2x^2- 4x+5 then find the values of 1/alpha + 1/beta

Answer 1

EXPLANATION.

→ a and b are the zeroes of the polynomial

p(x) = 2x² - 4x + 5

→ To find the value of → 1/a + 1/b.

→ sum of zeroes of quadratic polynomial.

a + b = -b/a

a + b = 4/2 = 2 ........(1)

→ products of zeroes of quadratic polynomial.

ab = c/a

ab = 5/2 .......(2)

→ 1/a + 1/b

→ b + a / ab

→ 2 / 5/2

→ 2/1 X 2/5

→ 4/5

→ Therefore,

→ value of 1/a + 1/b = 4/5.

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

If alpha and beta are the zeros of the polynomial p(x) = 2x^2- 4x+5 then find the values of 1/alpha + 1/beta

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

α and β are the zeros of the polynomial p(x) = 2x² + 3x + 5.

$\Large{\underline{\underline{\bf{Find :-}}}}$

The value of 1/α + 1/β.

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Here we go !

Sum of the zeros of a quadratic polynomial(ax² + bx + c) is

α + β = -coefficient of x/coefficient of x² = -b/a

Product of the zeros of a quadratic polynomial(ax² + bx + c) is

αβ =  constant term/coefficient of x² = c/a

Now,

The given equation is :-

2x²-4x+5..........

Here, a=2,b=-4,c=5

Now,

Since it is given that alpha and beta are the two zeroes of the polynomial. So, by formula we have :-

(alpha +beta) =-b/a=4/2=2. ............(i)

(alpha *beta) =c/a=5/2. .............(ii)

Now,

we have to find :-

1/alpha+1/beta

=(beta +Alfa) / alpha * beta

Now, putting values of eq (i) and (ii) , we get :-

2*2/5

=4/5

$\mathfrak{\huge{\pink{\underline{\underline{Hence}}}}}$

4/5 is the answer.