Question

Find a quadratic polynomial whose zeroes are 1 and _3 , verify the relation between the cofficient and zeroes of the polynomial

Answer 1

A quadratic polynomial whose zeroes are 1 and -3

Required polynomial = x2 - (sum of zeros) x + product of zeros

                               = x2 - (1-3) x + 1( -3)

                               = x2 + 2x - 3

Coefficient of x = 2 = sum of zeros

Constant term = -3 = product of zeros

Answer 2

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HERE'S THE ANSWER ✌
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The zeroes are given :-
1 and (-3)

Now
Sum of the zeroes is
1+(-3)=1-3 =(-2)....(i)

Now,
Product of the zeroes is
1*(-3)=(-3)....(ii).


Now,

We know that the form of any quadratic polynomial is
k(x^2- (sum of zeroes)x+ product)
So,.

Putting the values in the form mentioned above :-
k(x^2-(-2)x+(-3))
k(x^2+2x-3)
when k =1
polynomial becomes
x^2+2x-3.
.

Now,

The sum of zeroes is - b/a

That is - 2/1 = (-2)
Same as in.... (1)


Product of the zeroes is c/a

That is - 3/1 = (-3)
Same as in..... (2)


Hence,
The polynomial is (x²+2x-3)


Also, The relation between the zeroes and the coefficient of the quadratic polynomial is verified.

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