Question

find a quadratic polynomial whose one zero is 17 and sum of zeros is - 18

Answer 1

Hey friend

Here is your answer

GIVEN:

α = 17

LET THE OTHER ZERO BE β

SUM OF ZEROES = -18

α + β =-18

17+β=-18

β= -18-17

β= -35

PRODUCT OF ZEROES :

=αβ

=17×-35

= -595

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REQUIRED POLYNOMIAL :

=x²- (sum of zeroes)x+(product of zeroes)

=x²-(-18)x+(-595)

=x²+18x-595

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SO THE REQUIRED POLYNOMIAL IS x²+18x-595

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HOPE THIS HELPS YOU ☺

Answer 2

Hii Mate here is Your Answer,

Given :

The sum of two zeros = -18

$\alpha + \beta = - 18 \\ given \: \alpha = 17 \\ \alpha + \beta = - 18 \\ 17 + \beta = - 18 \\ \beta = - 35$
So, we need the required polynomial whose zeros are -35 and 17.

There is an formula for finding it and that formula is :

k [ x^2-( Sum of zeros)x + Product of zeros

So we will just substitute the value we will get :

${x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ {x}^{2} - ( 17 + ( - 35)) x+ 17 \times - 35 \\ {x}^{2} + 18 x- 595$
Therefore the required polynomial is
K(x^2+18x-595)

Here k is any constant number we can take any number here i take k = 1.

The answer is x^2+18x-595.

☆☆☆ HOPE THIS HELPS YOU A LOT ☆☆☆