Question

find a quadratic polynomial whose zeros are - 4 and 2

Answer 1

general form of quadratic equation is
x^2-(sum of roots)x+product of roots
x^2+2x-8

Answer 2

Answer:

Required quadratic polynomial

x²+2x-8

Explanation:

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

Here ,

$\alpha = -4, \beta = 2$

i ) Sum of the zeroes

= $\alpha+\beta$

= -4+2

= -2 ----(1)

ii) Product of the zeroes

= $\alpha\beta$

= (-4 )× 2

= -8 ----(2)

Therefore, the quadratic polynomial ax²+bx+c is

$k[x^{2}-(\alpha+\beta)x+\alpha\beta]$,

where k is a constant

=k[ x²-(-2)x+(-8)]

= k[x²+2x-8]

/* from (1) & (2) */

We can put different values of k.

When k=1 , the quadratic polynomial will be x²+2x-8.

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