Question

Find a quadratic polynomial whose one zero is root 5 and the product of the zeros is minus 2 root 5

Answer 1

Answer:

Hiiii friend,

Let Alpha and beta are the zeros of the Quadratic polynomial.

Alpha = 5

Product of zero = 30

(Alpha × Beta) = 30

5 × Beta = 30

Beta = 30/5 = 6

Alpha = 5 and Beta = 6

Therefore,

Sum of zeros = (Alpha + Beta) = (5+6) = 11

And,

Product of zeros = (Alpha × Beta) = (5×6) = 30

Therefore,

Required Quadratic polynomial = X²-(Alpha + Beta)X+Alpha × Beta

=> X²-(11)X +30

=> X²-11X+30

HOPE IT WILL HELP YOU........ :-)

Step-by-step explanation:

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Answer 2

Answer:

Let α=√5 and αβ= -2√5

Substituting α in αβ

√5β = -2√5

β= $\frac{-2\sqrt{5} }{\sqrt{5}}$

∴β=-2

and, α+β= √5+(-2) =√5-2

Hence, the quadratic polynomial so formed is,

=x² - (α+β)x + αβ

=x² - (√5-2)x + (-2√5)

=x² - (√5-2)x - 2√5

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