Question

form a quadratic polynomial whose zeroes are 5 and - 5.

Answer 1

Sum of zeroes = 5 - 5 = 02

Product of zeroes = 5(-5) = -25

Required polynomial = x^2 -(sum of zeroes)x + Product of zeroes

= x^2 - (0)x + ( -25)

= x^2 -25

Answer 2

Solution:

Let the quadratic polynomial be ax²+bx+c, a≠0 and it's zeroes be $\alpha \: and \: \beta .$

Here $\alpha = 5 \: and \: \beta = -5$

i ) Sum of the zeroes

= $\alpha+\beta$

= $5+(-5)$

= $5-5$

= 0

$\alpha+\beta = 0$---(1)

ii) product of the zeroes

= $\alpha\times\beta$

= $5\times (-5)$

=$-25$

$\alpha\beta=-25$---(2)

Therefore,

The quadratic polynomial ax²+bx+c is

$k[x^{2}-(\alpha+\beta)x+\alpha\beta], </p><p><em>where</em><em> </em><em>k</em><em> </em><em>is</em><em> </em><em>a</em><em> </em><em>cons</em><em>tant</em></p><p>=[tex]k[x^{2}-0\times x+(-25)]$

= $k(x^{2}-25)$

we can put different values of k.

When k=1,the quadratic polynomial will be x²-25.

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