Question

If alpha and beta are zeros of polynomial x^2-7x +10 , then form a quadratic polynomial whose zeros are half the zeros of the given polynomial

Answer 1

Answer:

zeroes of given polynomial: ---->

x square -7x +10.

x square -5x-2x+10.

x(x-5)-2(x-5).

(x-2)(x-5).

x=2 & 5 .

according to the question: --->

half of the zeroes is 1 & 5/2 .

as sum of the zeroes is 1+5/2=7/2 .

as product of zeroes is 1×5/2=5/2.

so the new equation is

x square -(sum if zeroes) x+product of zeroes.

x square -7/2x +5/2.

2x square -7x+5 =0. IS THE QUADRATIC POLYNOMIAL ...

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Answer 2

Let

p(x)=x2+7x+10

comparing with p(x)=ax2+bx+c

a=1,b=7,c=10

p(x)=x2+7x+10

⇒x2+5x+2x+10

⇒x(x+5)+2(x+5)

⇒(x+2)(x+5)

Let p(x)=0

⇒(x+2)(x+5)=0

x=−2,5

α=−2,β=−5

a−b=α+β⇒1−(7)=−7

ac=α⋅β⇒110=10