Question

if alpha and bitha are the zeroes of quadratic polynomial 2x^2+3x-5 find the value of 1/alpha +1/bitha
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Answer 1

Question :-

if α and β are the zeroes of quadratic polynomial 2x²+3x-5 find the value of 1/α + 1/β

Answer :-

1/α + 1/β = 3/5

Step-by-step explanation :-

       Given quadratic polynomial,

              2x² + 3x - 5

=>  It is of the form ax² + bx + c

        a = 2, b = 3, c = -5

a - coefficient of x²

b - coefficient of x

c - constant term

By sum-product pattern,

>> Find the product of quadratic term [ax²] and constant term [c]

  = 2x² × (-5)

  = -10x²

>> find the factors of "-10x²" in pairs

    => (x) (-10x)

    => (-x) (10x)

    => (2x) (-5x)

    => (-2x) (5x)

>> From the above, find the pair that adds to get linear term [bx]

     5x - 2x = 3x

>> So, split 3x as 5x and -2x

        2x² + 3x - 5 = 0

    2x² - 2x + 5x - 5 = 0

>> Find the common factor

       2x(x - 1) + 5(x - 1) = 0

        (x - 1) (2x + 5) =  0

=> x - 1 = 0 ; x = +1

=> 2x + 5 = 0 ; x = -5/2

1 and -5/2 are the zeroes of the polynomial.

Let

α = 1

β = -5/2

$=\frac{1}{\alpha} +\frac{1}{\beta} \\\\ =\frac{\alpha + \beta}{\alpha \beta} \\\\ =\frac{1-\frac{5}{2} }{(1)(\frac{-5}{2})} \\\\ =\frac{\frac{2-5}{2}}{\frac{-5}{2}} \\\\ =\frac{\frac{-3}{2}}{\frac{-5}{2}} \\\\ =\frac{3}{5}$

$\boxed{\bf \therefore \frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{5}}$

Answer 2

Refer the attachment............