Question

21. Write the quadratic polynomial, whose sum of zeroes is – 3 and sum of the squares of zeroes is 17.

Answer 1

Step-by-step explanation:

let the zeros of the quadratic polynomial be x and y and quadratic polynomial be ax^2+bx+c

so, x+y=-3----------(¡)

x^2+y^2=17---------(¡¡)

(¡)=>x=-3-y

substituting the value in (¡) in equation (¡¡),we have:

(-3-y)^2+y^2=17

=>9+y^2+6y+y^2=17

=>2y^2+6y+9-17=0

=>2y^2+6y-8=0

=>(2y-2)(y+4)=0

so, 2y-2=0 or y+4=0

=>y=2/2 or y=-4

so, y=1or-4

now, substituting y=1in (¡)

x+1=-3

=>x=-4

again, substituting y=-4 in (¡)

x-4=3

=>x=7

therefore, zeroes of polynomial are 1and-3 or-4 and 7

Answer 2

Step

Let a and b are the roots.

  According to the question:

a + b = - 3

⇒ a^2 + b^2 = 17

⇒ a^2 + b^2 + 2ab - 2ab = 17

⇒ ( a + b )^2 - 2ab = 17

⇒ ( - 3 )^2 - 2ab = 17

⇒ 9 - 2ab = 17

⇒ 9 - 17 = 2ab

⇒ - 8 = 2ab

⇒ - 4 = ab = product of roots.

   Hence,

Req. pol. is x^2 - ( sum of roots )x + product of roots

⇒ x^2 - ( a + b )x + ab

⇒ x^2 - ( - 3 )x + ( - 4 )

⇒ x^2 + 3x - 4