Question

2. The sum and product of the zeroes of a quadratic polynomial are 3 and -10 respectively. The quadratic
polynomial is

Answer 1

Answer:

If α, β be the zeros of the quadratic polynomial ,then

(x−α)(x−β) is the quadratic polynomial.

Thus, (x−α)(x−β) is the polynomial.

=x

2

−αx−βx+αβ

=x

2

−x(α+β)+αβ(i)

(α+β)=−5αβ=3

Now putting the value of (α+β),αβ in equation (i) we get,

x

2

−x(−5)+3

=x

2

+5x+3.

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Answer 2

Answer:

The Quadratic polynomial will be x^2-3x-10

Step-by-step explanation:

Let the quadratic polynomial be ax ^2+bx+c and its zeros be α and β.

STEP 1: Sum of zeros = α+β = 3 = − b/a

STEP 2: Product of zeros = αβ = -10 = c/a

STEP 3:  If a=1, then b= -3 and c= -10

STEP 4 : Hence,  one quadratic polynomial will be x^2-3x-10