Question

let alpha and beta are the zeros of quadratic polynomial 2×^2-5×-6 then form a quadratic polynomial whose zeros are alpha + beta and alpha multiply beta

Answer 1

Explanation:

Compare 2x²-5x-6 with ax²+bx+c we get,

a = 2 , b = -5 , c = -6

Given$\alpha\: and\: \beta$ are zeroes of the polyomial

i ) sum of the zeroes = -b/a

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

= $\frac{5}{2}$---(1)

ii) product of the zeroes = c/a

$\alpha\beta = \frac{-6}{2}$

= -3---(2)

Now ,

If $\alpha+\beta ,\: \alpha\beta$ are zeroes ,

iii) Sum of the zeroes=

$\alpha+\beta+\alpha\beta</p><p>=\frac{5}{2}-3$

= $\frac{5-6}{2}$

=$\frac{-1}{2}$---(3)

iv) product of the roots

= $\frac{5}{2}\times(-3)$

= $\frac{-15}{2}$---(4)

__________________________

we know the form of Quadratic polynomial in variable x is

k[x²-(sum of the zeroes)x+product of the zeroes]

_________________________

Now ,

k[x²-(-1/2)x+(-15/2)]

For all real values of k it is true,

Let k = 2 ,

Required polynomial is

2[x²+(1/2)x-(15/2)]

= 2x²+x-15

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Answer 2

Answer:

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