If alpha and - are zeroes of polynomial x2-6 x-9- then form a quadratic polynomial whose zeroes are -alpha- -

If alpha and ß are zeroes of polynomial x²+6x+9 then alpha * ß(product of zeroes) =c/a =9/1 =9= gt;alpha * ß=9 —(1) alpha * ß(sum of zeroes) = b/a = 6/1 = ...

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Standard X

Mathematics

Formation of a Quadratic Equation From It's Roots

If alpha and ...

Question

If alpha and ß are zeroes of polynomial x²+6x+9, then form a quadratic polynomial whose zeroes are -alpha, -ß.

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Solution

If alpha and ß are zeroes of polynomial x²+6x+9

then alpha * ß(product of zeroes) =c/a =9/1 =9=>alpha * ß=9 ---(1)

alpha * ß(sum of zeroes) =-b/a =-6/1 =-6 =>alpha + ß= -6 ----(2)

Now zeroes of new quadratic equation are -alpha, -ß.

sum of zeroes = -alpha+ -ß = -(alpha + ß)

from (2) = --6 =6 ---(3)

product of zeroes = -alpha * -ß = -alpha * -ß =alpha * ß

from (1) = 9 ----(4)

Quadratic equation if of the form x² -(sum of zeroes)x +product of zeroes

=x² -(6)x + 9

=x² -6x + 9

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