Question

if alpha and beta are the zeroes of the quadratic polynomial 3x^2 + 5x - 2, then find the value of 1/alpha + 1/beta​

Answer 1

Answer:

5/2

Step-by-step explanation:

Let alpha be a and beta be b

from given information, a,b are the zeros of the equation

3x*2+5x-2

=> we have sum of zeros is -( x coefficient)/ coefficient of x*2

=> we also have product of zeros is constant/ coefficient of x*2

by above information we have ,

a+ b = -5/3,

ab= -2/3

we need , 1/a+ 1/b

by simplyfing this. we get 1/a+1/ b =( a+b)/ab

=( -5/3)/(-2/3)

= 5/2

therefore we have 1)a+1/b = 5/2

Answer 2

S O L U T I O N :

We have quadratic polynomial p(x) = 3x² + 5x - 2 & zero of the polynomial p(x) = 0.

Using by factorization method :

→ 3x² + 5x - 2 = 0

→ 3x² +6x - x - 2 = 0

→ 3x(x + 2) -1(x + 2) = 0

→ (x + 2) (3x - 1) = 0

→ x + 2 = 0  Or  3x - 1 = 0

→ x = -2  Or  3x = 1

→ x = -2  Or  x = 1/3

∴ α = -2 & β = 1/3 are two zeroes of the given polynomial .

Now,

$\longrightarrow\tt{\dfrac{1}{\alpha } + \dfrac{1}{\beta } }$

$\longrightarrow\tt{\dfrac{\alpha +\beta}{\alpha \beta } }$

$\longrightarrow\tt{\dfrac{-2 + 1/3}{-2 \times 1/3} }$

$\longrightarrow\tt{\dfrac{-6 + 1/3}{-2/3} }$

$\longrightarrow\tt{\dfrac{-5/3}{-2/3} }$

$\longrightarrow\tt{\dfrac{-5}{\cancel{3}} \times \dfrac{\cancel{3}}{-2} }$

$\longrightarrow\tt{\dfrac{-5}{-2} }$

$\longrightarrow\bf{5/2}$

Thus,

The value of 1/α + 1/β will be 5/2 .