Question

if a and b are the zeroes of the polynomial x2+7x+7 then find the value of a2+ b2​

Answer 1

Answer:

p(x)= x^2+7x+7

x^2+7x+7=0

Do it by quadratic formula

a=1,b=7,c=7

d=b^2-4ac

d=7^2-4(1)(7)

d=49-28

d=21

x=-b+√d/2a

and

x = -b-√d/2a. ( bcoz in a quadratic equation there are two roots)

so,

x= -7+ √21/2(1)= -7+√21/2

and

x=-7 -√21/2

Hope it helps!!

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Answer 2

Answer:

a2 + b2= 35

Step-by-step explanation:

let a and b be the zeroes of the polynomial.

then, sum of zeroes = a + b = -(coeficient of x)/coefficient of x2.

so, a +b = -7/1 = -7 -(i)

now,

product of zeroes = ab = constant/ coefficient of x2.

so, ab = 7/1 =7 -(ii)

now, We know that (a+b)2 = a2 + b2 + 2ab

we have to find value of a2 + b2 , so keep it on one side and send else on another side.

now,

a2 + b2 = (a + b)2 - 2ab.

a2 + b2 = (-7)2 - 2(7)

a2 + b2 = 49 - 14

a2 + b2 = 35. which is the answer.

hope it all clear

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